13776a006a
4db0a62 bugfix of lazy prepare 87017bd license dc703e1 license c171440 change license to bsd 7db2070 Update README.md 581fe06 add mocktest d2f252f ok 4a5b9e5 add all 12ee049 init version of lbfgs 37a2837 complete lbfgs solver 6ade7cb complete lbfgs git-subtree-dir: subtree/rabit git-subtree-split: 4db0a62a068894a55f70bad5e80c33d4434fc834
654 lines
21 KiB
C++
654 lines
21 KiB
C++
/*!
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* Copyright (c) 2015 by Contributors
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* \file lbfgs.h
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* \brief L-BFGS solver for general optimization problem
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*
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* \author Tianqi Chen
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*/
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#ifndef RABIT_LEARN_LBFGS_H_
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#define RABIT_LEARN_LBFGS_H_
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#include <cmath>
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#include <rabit.h>
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namespace rabit {
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/*! \brief namespace of solver for general problems */
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namespace solver {
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/*!
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* \brief objective function for optimizers
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* the objective function can also implement save/load
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* to remember the state parameters that might need to remember
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*/
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template<typename DType>
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class IObjFunction : public rabit::ISerializable {
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public:
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// destructor
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virtual ~IObjFunction(void){}
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/*!
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* \brief evaluate function values for a given weight
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* \param weight weight of the function
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* \param size size of the weight
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*/
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virtual double Eval(const DType *weight, size_t size) = 0;
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/*!
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* \return number of feature dimension to be allocated
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* only called once during initialization
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*/
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virtual size_t InitNumDim(void) = 0;
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/*!
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* \brief initialize the weight before starting the solver
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* only called once for initialization
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*/
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virtual void InitModel(DType *weight, size_t size) = 0;
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/*!
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* \brief calculate gradient for a given weight
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* \param out_grad used to store the gradient value of the function
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* \param weight weight of the function
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* \param size size of the weight
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*/
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virtual void CalcGrad(DType *out_grad,
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const DType *weight,
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size_t size) = 0;
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};
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/*! \brief a basic version L-BFGS solver */
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template<typename DType>
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class LBFGSSolver {
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public:
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LBFGSSolver(void) {
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// set default values
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reg_L1 = 0.0f;
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max_linesearch_iter = 100;
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linesearch_backoff = 0.5f;
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linesearch_c1 = 1e-4;
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min_lbfgs_iter = 5;
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max_lbfgs_iter = 500;
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lbfgs_stop_tol = 1e-5f;
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silent = 0;
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}
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virtual ~LBFGSSolver(void) {}
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/*!
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* \brief set parameters from outside
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* \param name name of the parameter
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* \param val value of the parameter
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*/
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virtual void SetParam(const char *name, const char *val) {
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if (!strcmp("num_dim", name)) {
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gstate.num_dim = static_cast<size_t>(atol(val));
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}
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if (!strcmp("size_memory", name)) {
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gstate.size_memory = static_cast<size_t>(atol(val));
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}
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if (!strcmp("reg_L1", name)) {
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reg_L1 = static_cast<float>(atof(val));
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}
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if (!strcmp("lbfgs_stop_tol", name)) {
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lbfgs_stop_tol = static_cast<float>(atof(val));
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}
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if (!strcmp("linesearch_backoff", name)) {
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linesearch_backoff = static_cast<float>(atof(val));
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}
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if (!strcmp("max_linesearch_iter", name)) {
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max_linesearch_iter = atoi(val);
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}
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if (!strcmp("max_lbfgs_iter", name)) {
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max_lbfgs_iter = atoi(val);
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}
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if (!strcmp("min_lbfgs_iter", name)) {
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min_lbfgs_iter = atoi(val);
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}
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if (!strcmp("linesearch_c1", name)) {
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linesearch_c1 = static_cast<float>(atof(val));
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}
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}
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/*!
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* \brief set objective function to optimize
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* the objective function only need to evaluate and calculate
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* gradient with respect to current subset of data
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* \param obj the objective function we are looking for
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*/
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virtual void SetObjFunction(IObjFunction<DType> *obj) {
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gstate.obj = obj;
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}
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/*!
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* \brief initialize the LBFGS solver
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* user must already set the objective function
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*/
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virtual void Init(void) {
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utils::Check(gstate.obj != NULL,
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"LBFGSSolver.Init must SetObjFunction first");
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int version = rabit::LoadCheckPoint(&gstate, &hist);
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if (version == 0) {
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gstate.num_dim = gstate.obj->InitNumDim();
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} else {
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printf("restart from version=%d\n", version);
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}
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{
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// decide parameter partition
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size_t nproc = rabit::GetWorldSize();
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size_t rank = rabit::GetRank();
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size_t step = (gstate.num_dim + nproc - 1) / nproc;
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// upper align
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step = (step + 7) / 8 * 8;
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utils::Assert(step * nproc >= gstate.num_dim, "BUG");
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range_begin_ = std::min(rank * step, gstate.num_dim);
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range_end_ = std::min((rank + 1) * step, gstate.num_dim);
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}
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if (version == 0) {
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gstate.Init();
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hist.Init(range_end_ - range_begin_, gstate.size_memory);
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gstate.obj->InitModel(gstate.weight, gstate.num_dim);
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// broadcast initialize model
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rabit::Broadcast(gstate.weight,
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sizeof(DType) * gstate.num_dim, 0);
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gstate.old_objval = this->Eval(gstate.weight);
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gstate.init_objval = gstate.old_objval;
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if (silent == 0 && rabit::GetRank() == 0) {
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rabit::TrackerPrintf
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("L-BFGS solver starts, num_dim=%lu, init_objval=%g, size_memory=%lu\n",
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gstate.num_dim, gstate.init_objval, gstate.size_memory);
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}
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}
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}
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/*!
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* \brief get the current weight vector
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* note that if update function is called
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* the content of weight vector is no longer valid
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* \return weight vector
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*/
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virtual DType *GetWeight(void) {
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return gstate.weight;
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}
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/*!
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* \brief update the weight for one L-BFGS iteration
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* \return whether stopping condition is met
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*/
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virtual bool UpdateOneIter(void) {
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bool stop = false;
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GlobalState &g = gstate;
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g.obj->CalcGrad(g.grad, g.weight, g.num_dim);
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rabit::Allreduce<rabit::op::Sum>(g.grad, g.num_dim);
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// find change direction
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double vdot = FindChangeDirection(g.tempw, g.grad, g.weight);
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// line-search, g.grad is now new weight
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int iter = BacktrackLineSearch(g.grad, g.tempw, g.weight, vdot);
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utils::Check(iter < max_linesearch_iter, "line search failed");
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// swap new weight
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std::swap(g.weight, g.grad);
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// check stop condition
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if (gstate.num_iteration > min_lbfgs_iter) {
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if (g.old_objval - g.new_objval < lbfgs_stop_tol * g.init_objval) {
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return true;
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}
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}
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if (silent == 0 && rabit::GetRank() == 0) {
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rabit::TrackerPrintf
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("[%d] L-BFGS: linesearch finishes in %d rounds, new_objval=%g, improvment=%g\n",
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gstate.num_iteration, iter,
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gstate.new_objval,
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gstate.old_objval - gstate.new_objval);
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}
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gstate.old_objval = gstate.new_objval;
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rabit::CheckPoint(&gstate, &hist);
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return stop;
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}
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/*! \brief run optimization */
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virtual void Run(void) {
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this->Init();
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while (gstate.num_iteration < max_lbfgs_iter) {
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if (this->UpdateOneIter()) break;
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}
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if (silent == 0 && rabit::GetRank() == 0) {
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size_t nonzero = 0;
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for (size_t i = 0; i < gstate.num_dim; ++i) {
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if (gstate.weight[i] != 0.0f) nonzero += 1;
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}
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rabit::TrackerPrintf
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("L-BFGS: finishes at iteration %d, %lu/%lu active weights\n",
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gstate.num_iteration, nonzero, gstate.num_dim);
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}
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}
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protected:
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// find the delta value, given gradient
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// return dot(dir, l1grad)
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virtual double FindChangeDirection(DType *dir,
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const DType *grad,
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const DType *weight) {
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int m = static_cast<int>(gstate.size_memory);
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int n = static_cast<int>(hist.num_useful());
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if (n < m) {
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utils::Assert(hist.num_useful() == gstate.num_iteration,
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"BUG2, n=%d, it=%d", n, gstate.num_iteration);
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} else {
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utils::Assert(n == m, "BUG3");
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}
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const size_t num_dim = gstate.num_dim;
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const DType *gsub = grad + range_begin_;
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const size_t nsub = range_end_ - range_begin_;
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double vdot;
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if (n != 0) {
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// hist[m + n - 1] stores old gradient
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Minus(hist[m + n - 1], gsub, hist[m + n - 1], nsub);
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SetL1Dir(hist[2 * m], gsub, weight + range_begin_, nsub);
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// index set for calculating results
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std::vector<std::pair<size_t, size_t> > idxset;
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for (int j = 0; j < n; ++j) {
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idxset.push_back(std::make_pair(j, 2 * m));
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idxset.push_back(std::make_pair(j, n - 1));
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idxset.push_back(std::make_pair(j, m + n - 1));
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}
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for (int j = 0; j < n; ++j) {
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idxset.push_back(std::make_pair(m + j, 2 * m));
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idxset.push_back(std::make_pair(m + j, m + n - 1));
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}
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// calculate dot products
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std::vector<double> tmp(idxset.size());
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for (size_t i = 0; i < tmp.size(); ++i) {
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tmp[i] = hist.CalcDot(idxset[i].first, idxset[i].second);
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}
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rabit::Allreduce<rabit::op::Sum>(BeginPtr(tmp), tmp.size());
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for (size_t i = 0; i < tmp.size(); ++i) {
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gstate.DotBuf(idxset[i].first, idxset[i].second) = tmp[i];
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}
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// BFGS steps, use vector-free update
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// parameterize vector using basis in hist
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std::vector<double> alpha(n);
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std::vector<double> delta(2 * m + 1, 0.0);
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delta[2 * m] = 1.0;
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// backward step
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for (int j = n - 1; j >= 0; --j) {
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double vsum = 0.0;
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for (size_t k = 0; k < delta.size(); ++k) {
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vsum += delta[k] * gstate.DotBuf(k, j);
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}
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alpha[j] = vsum / gstate.DotBuf(j, m + j);
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delta[m + j] = delta[m + j] - alpha[j];
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}
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// scale
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double scale = gstate.DotBuf(n - 1, m + n - 1) /
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gstate.DotBuf(m + n - 1, m + n - 1);
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for (size_t k = 0; k < delta.size(); ++k) {
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delta[k] *= scale;
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}
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// forward step
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for (int j = 0; j < n; ++j) {
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double vsum = 0.0;
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for (size_t k = 0; k < delta.size(); ++k) {
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vsum += delta[k] * gstate.DotBuf(k, m + j);
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}
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double beta = vsum / gstate.DotBuf(j, m + j);
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delta[j] = delta[j] + (alpha[j] - beta);
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}
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// set all to zero
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std::fill(dir, dir + num_dim, 0.0f);
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DType *dirsub = dir + range_begin_;
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for (int i = 0; i < n; ++i) {
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AddScale(dirsub, dirsub, hist[m + i], delta[m + i], nsub);
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}
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AddScale(dirsub, dirsub, hist[2 * m], delta[2 * m], nsub);
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for (int i = 0; i < n; ++i) {
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AddScale(dirsub, dirsub, hist[i], delta[i], nsub);
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}
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FixDirL1Sign(dirsub, hist[2 * m], nsub);
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vdot = -Dot(dirsub, hist[2 * m], nsub);
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// allreduce to get full direction
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rabit::Allreduce<rabit::op::Sum>(dir, num_dim);
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rabit::Allreduce<rabit::op::Sum>(&vdot, 1);
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} else {
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SetL1Dir(dir, grad, weight, num_dim);
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vdot = -Dot(dir, dir, num_dim);
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}
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// shift the history record
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if (n < m) {
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n += 1;
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} else {
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gstate.Shift(); hist.Shift();
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}
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hist.set_num_useful(n);
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// copy gradient to hist[m + n - 1]
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memcpy(hist[m + n - 1], gsub, nsub * sizeof(DType));
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return vdot;
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}
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// line search for given direction
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// return whether there is a descent
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inline int BacktrackLineSearch(DType *new_weight,
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const DType *dir,
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const DType *weight,
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double dot_dir_l1grad) {
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utils::Assert(dot_dir_l1grad < 0.0f,
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"gradient error, dotv=%g", dot_dir_l1grad);
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double alpha = 1.0;
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double backoff = linesearch_backoff;
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// unit descent direction in first iter
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if (gstate.num_iteration == 0) {
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utils::Assert(hist.num_useful() == 1, "hist.nuseful");
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alpha = 1.0f / std::sqrt(-dot_dir_l1grad);
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backoff = 0.1f;
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}
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int iter = 0;
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double old_val = gstate.old_objval;
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double c1 = this->linesearch_c1;
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while (true) {
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const size_t num_dim = gstate.num_dim;
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if (++iter >= max_linesearch_iter) return iter;
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AddScale(new_weight, weight, dir, alpha, num_dim);
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this->FixWeightL1Sign(new_weight, weight, num_dim);
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double new_val = this->Eval(new_weight);
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if (new_val - old_val <= c1 * dot_dir_l1grad * alpha) {
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gstate.new_objval = new_val; break;
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}
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alpha *= backoff;
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}
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// hist[n - 1] = new_weight - weight
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Minus(hist[hist.num_useful() - 1],
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new_weight + range_begin_,
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weight + range_begin_,
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range_end_ - range_begin_);
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gstate.num_iteration += 1;
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return iter;
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}
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// OWL-QN step for L1 regularization
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inline void SetL1Dir(DType *dst,
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const DType *grad,
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const DType *weight,
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size_t size) {
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if (reg_L1 == 0.0) {
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for (size_t i = 0; i < size; ++i) {
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dst[i] = -grad[i];
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}
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} else {
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for (size_t i = 0; i < size; ++i) {
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if (weight[i] > 0.0f) {
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dst[i] = -grad[i] - reg_L1;
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} else if (weight[i] < 0.0f) {
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dst[i] = -grad[i] + reg_L1;
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} else {
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if (grad[i] < -reg_L1) {
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dst[i] = -grad[i] - reg_L1;
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} else if (grad[i] > reg_L1) {
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dst[i] = -grad[i] + reg_L1;
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} else {
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dst[i] = 0.0;
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}
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}
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}
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}
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}
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// OWL-QN step: fix direction sign to be consistent with proposal
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inline void FixDirL1Sign(DType *dir,
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const DType *steepdir,
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size_t size) {
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if (reg_L1 != 0.0f) {
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for (size_t i = 0; i < size; ++i) {
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if (dir[i] * steepdir[i] <= 0.0f) {
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dir[i] = 0.0f;
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}
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}
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}
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}
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// QWL-QN step: fix direction sign to be consistent with proposal
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inline void FixWeightL1Sign(DType *new_weight,
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const DType *weight,
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size_t size) {
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if (reg_L1 != 0.0f) {
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for (size_t i = 0; i < size; ++i) {
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if (new_weight[i] * weight[i] < 0.0f) {
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new_weight[i] = 0.0f;
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}
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}
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}
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}
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inline double Eval(const DType *weight) {
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double val = gstate.obj->Eval(weight, gstate.num_dim);
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rabit::Allreduce<rabit::op::Sum>(&val, 1);
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if (reg_L1 != 0.0f) {
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double l1norm = 0.0;
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for (size_t i = 0; i < gstate.num_dim; ++i) {
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l1norm += std::abs(weight[i]);
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}
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val += l1norm * reg_L1;
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}
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return val;
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}
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private:
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// helper functions
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// dst = lhs + rhs * scale
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inline static void AddScale(DType *dst,
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const DType *lhs,
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const DType *rhs,
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DType scale,
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size_t size) {
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for (size_t i = 0; i < size; ++i) {
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dst[i] = lhs[i] + rhs[i] * scale;
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}
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}
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// dst = lhs - rhs
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inline static void Minus(DType *dst,
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const DType *lhs,
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const DType *rhs,
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size_t size) {
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for (size_t i = 0; i < size; ++i) {
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dst[i] = lhs[i] - rhs[i];
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}
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}
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// return dot(lhs, rhs)
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inline static double Dot(const DType *lhs,
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const DType *rhs,
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size_t size) {
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double res = 0.0;
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for (size_t i = 0; i < size; ++i) {
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res += lhs[i] * rhs[i];
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}
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return res;
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}
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// map rolling array index
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inline static size_t MapIndex(size_t i, size_t offset,
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size_t size_memory) {
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if (i == 2 * size_memory) return i;
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if (i < size_memory) {
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return (i + offset) % size_memory;
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} else {
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utils::Assert(i < 2 * size_memory,
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"MapIndex: index exceed bound, i=%lu", i);
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return (i + offset) % size_memory + size_memory;
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}
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|
}
|
|
// global solver state
|
|
struct GlobalState : public rabit::ISerializable {
|
|
public:
|
|
// memory size of L-BFGS
|
|
size_t size_memory;
|
|
// number of iterations passed
|
|
size_t num_iteration;
|
|
// number of features in the solver
|
|
size_t num_dim;
|
|
// initialize objective value
|
|
double init_objval;
|
|
// history objective value
|
|
double old_objval;
|
|
// new objective value
|
|
double new_objval;
|
|
// objective function
|
|
IObjFunction<DType> *obj;
|
|
// temporal storage
|
|
DType *grad, *weight, *tempw;
|
|
// constructor
|
|
GlobalState(void)
|
|
: obj(NULL), grad(NULL),
|
|
weight(NULL), tempw(NULL) {
|
|
size_memory = 10;
|
|
num_iteration = 0;
|
|
num_dim = 0;
|
|
old_objval = 0.0;
|
|
}
|
|
~GlobalState(void) {
|
|
if (grad != NULL) {
|
|
delete [] grad;
|
|
delete [] weight;
|
|
delete [] tempw;
|
|
}
|
|
}
|
|
// intilize the space of rolling array
|
|
inline void Init(void) {
|
|
size_t n = size_memory * 2 + 1;
|
|
data.resize(n * n, 0.0);
|
|
this->AllocSpace();
|
|
}
|
|
inline double &DotBuf(size_t i, size_t j) {
|
|
if (i > j) std::swap(i, j);
|
|
return data[MapIndex(i, offset_, size_memory) * (size_memory * 2 + 1) +
|
|
MapIndex(j, offset_, size_memory)];
|
|
}
|
|
// load the shift array
|
|
virtual void Load(rabit::IStream &fi) {
|
|
fi.Read(&size_memory, sizeof(size_memory));
|
|
fi.Read(&num_iteration, sizeof(num_iteration));
|
|
fi.Read(&num_dim, sizeof(num_dim));
|
|
fi.Read(&init_objval, sizeof(init_objval));
|
|
fi.Read(&old_objval, sizeof(old_objval));
|
|
fi.Read(&offset_, sizeof(offset_));
|
|
fi.Read(&data);
|
|
this->AllocSpace();
|
|
fi.Read(weight, sizeof(DType) * num_dim);
|
|
obj->Load(fi);
|
|
}
|
|
// save the shift array
|
|
virtual void Save(rabit::IStream &fo) const {
|
|
fo.Write(&size_memory, sizeof(size_memory));
|
|
fo.Write(&num_iteration, sizeof(num_iteration));
|
|
fo.Write(&num_dim, sizeof(num_dim));
|
|
fo.Write(&init_objval, sizeof(init_objval));
|
|
fo.Write(&old_objval, sizeof(old_objval));
|
|
fo.Write(&offset_, sizeof(offset_));
|
|
fo.Write(data);
|
|
fo.Write(weight, sizeof(DType) * num_dim);
|
|
obj->Save(fo);
|
|
}
|
|
inline void Shift(void) {
|
|
offset_ = (offset_ + 1) % size_memory;
|
|
}
|
|
|
|
private:
|
|
// rolling offset in the current memory
|
|
size_t offset_;
|
|
std::vector<double> data;
|
|
// allocate sapce
|
|
inline void AllocSpace(void) {
|
|
if (grad == NULL) {
|
|
grad = new DType[num_dim];
|
|
weight = new DType[num_dim];
|
|
tempw = new DType[num_dim];
|
|
}
|
|
}
|
|
};
|
|
/*! \brief rolling array that carries history information */
|
|
struct HistoryArray : public rabit::ISerializable {
|
|
public:
|
|
HistoryArray(void) : dptr_(NULL) {
|
|
num_useful_ = 0;
|
|
}
|
|
~HistoryArray(void) {
|
|
if (dptr_ != NULL) delete [] dptr_;
|
|
}
|
|
// intilize the space of rolling array
|
|
inline void Init(size_t num_col, size_t size_memory) {
|
|
if (dptr_ != NULL &&
|
|
(num_col_ != num_col || size_memory_ != size_memory)) {
|
|
delete dptr_;
|
|
}
|
|
num_col_ = num_col;
|
|
size_memory_ = size_memory;
|
|
stride_ = num_col_;
|
|
offset_ = 0;
|
|
size_t n = size_memory * 2 + 1;
|
|
dptr_ = new DType[n * stride_];
|
|
}
|
|
// fetch element from rolling array
|
|
inline const DType *operator[](size_t i) const {
|
|
return dptr_ + MapIndex(i, offset_, size_memory_) * stride_;
|
|
}
|
|
inline DType *operator[](size_t i) {
|
|
return dptr_ + MapIndex(i, offset_, size_memory_) * stride_;
|
|
}
|
|
// shift array: arr_old -> arr_new
|
|
// for i in [0, size_memory - 1), arr_new[i] = arr_old[i + 1]
|
|
// for i in [size_memory, 2 * size_memory - 1), arr_new[i] = arr_old[i + 1]
|
|
// arr_old[0] and arr_arr[size_memory] will be discarded
|
|
inline void Shift(void) {
|
|
offset_ = (offset_ + 1) % size_memory_;
|
|
}
|
|
inline double CalcDot(size_t i, size_t j) const {
|
|
return Dot((*this)[i], (*this)[j], num_col_);
|
|
}
|
|
// set number of useful memory
|
|
inline const size_t &num_useful(void) const {
|
|
return num_useful_;
|
|
}
|
|
// set number of useful memory
|
|
inline void set_num_useful(size_t num_useful) {
|
|
utils::Assert(num_useful <= size_memory_,
|
|
"num_useful exceed bound");
|
|
num_useful_ = num_useful;
|
|
}
|
|
// load the shift array
|
|
virtual void Load(rabit::IStream &fi) {
|
|
fi.Read(&num_col_, sizeof(num_col_));
|
|
fi.Read(&stride_, sizeof(stride_));
|
|
fi.Read(&size_memory_, sizeof(size_memory_));
|
|
fi.Read(&num_useful_, sizeof(num_useful_));
|
|
this->Init(num_col_, size_memory_);
|
|
for (size_t i = 0; i < num_useful_; ++i) {
|
|
fi.Read((*this)[i], num_col_ * sizeof(DType));
|
|
fi.Read((*this)[i + size_memory_], num_col_ * sizeof(DType));
|
|
}
|
|
}
|
|
// save the shift array
|
|
virtual void Save(rabit::IStream &fi) const {
|
|
fi.Write(&num_col_, sizeof(num_col_));
|
|
fi.Write(&stride_, sizeof(stride_));
|
|
fi.Write(&size_memory_, sizeof(size_memory_));
|
|
fi.Write(&num_useful_, sizeof(num_useful_));
|
|
for (size_t i = 0; i < num_useful_; ++i) {
|
|
fi.Write((*this)[i], num_col_ * sizeof(DType));
|
|
fi.Write((*this)[i + size_memory_], num_col_ * sizeof(DType));
|
|
}
|
|
}
|
|
|
|
private:
|
|
// number of columns in each of array
|
|
size_t num_col_;
|
|
// stride for each of column for alignment
|
|
size_t stride_;
|
|
// memory size of L-BFGS
|
|
size_t size_memory_;
|
|
// number of useful memory that will be used
|
|
size_t num_useful_;
|
|
// rolling offset in the current memory
|
|
size_t offset_;
|
|
// data pointer
|
|
DType *dptr_;
|
|
};
|
|
// data structure for LBFGS
|
|
GlobalState gstate;
|
|
HistoryArray hist;
|
|
// silent
|
|
int silent;
|
|
// the subrange of current node
|
|
size_t range_begin_;
|
|
size_t range_end_;
|
|
// L1 regularization co-efficient
|
|
float reg_L1;
|
|
// c1 ratio for line search
|
|
float linesearch_c1;
|
|
float linesearch_backoff;
|
|
int max_linesearch_iter;
|
|
int max_lbfgs_iter;
|
|
int min_lbfgs_iter;
|
|
float lbfgs_stop_tol;
|
|
};
|
|
} // namespace solver
|
|
} // namespace rabit
|
|
#endif // RABIT_LEARN_LBFGS_H_
|