Finite-sample analysis of proximal gradient td algorithms pdf

Finitesample analysis of lasso td gorithmic work on adding 1penalties to the td loth et al. Marek petrik college of engineering and physical sciences. Convergent tree backup and retrace with function approximation. As a byproduct of our analysis, we also obtain an improved sample complexity bound for the rank centrality algorithm to recover an optimal ranking under a bradleyterryluce btl condition, which answers an open question of rajkumar and agarwal. In general, stochastic primaldual gradient algorithms like the ones derived in this paper can be shown to achieve o 1 k convergence rate where k is the number of iterations. C10 bo liu, ji liu, mohammad ghavamzadeh, sridhar mahadevan, marek petrik. These seem to me to be the best attempts to make td methods with the robust convergence properties of stochastic gradient descent. Congratulations to our recent alumni academic hires. Investigating practical linear temporal difference learning. The proximal gradient algorithm minimizes f iteratively, with each iteration consisting of 1.

Based on our analysis, we then derive stable and efficient gradient based algorithms, compatible with accumulating or dutch traces, using a novel methodology based on proximal methods. Previous analyses of this class of algorithms use stochastic approximation techniques to prove asymptotic convergence, and do not provide any finitesample analysis. Proximal gradient algorithms proximal algorithms are particularly useful when the functional we are minimizing can be broken into two parts, one of which is smooth, and the other for which there is a fast proximal operator. High confidence policy improvement proceedings of the 32nd international conference on machine learning icml, 2015. In this paper, we introduce proximal gradient temporal difference learning, which provides a principled way of designing and analyzing true stochastic gradient temporal difference learning algorithms. On generalized bellman equations and temporaldifference learning. In this work, we introduce a new family of targetbased temporal difference td learning algorithms and provide theoretical analysis on their convergences. On the finitetime convergence of actorcritic algorithm. Bo liu, ji liu, mohammad ghavamzadeh, sridhar mahadevan, and marek petrik. Td0 is one of the most commonly used algorithms in reinforcement learning. Proceedings of the conference on uncertainty in ai uai, 2015, facebook best student paper award. Autonomous learning laboratory, barto and mahadevan.

Boliu, ji liu, mohammadghavamzadeh, sridharmahadevan, marekpetrik 504 estimatingthe partition function by discriminance sampling. Finite sample analysisof proximal gradient tdalgorithms. Finitesample analysis of proximal gradient td algorithms proceedings of the thirtyfirst conference on uncertainty in artificial intelligence uai2015, pp. Two novel algorithms are proposed to approximate the true value function v. Two novel gtd algorithms are also proposed, namely projected gtd2 and gtd2mp, which use proximal mirror maps to yield improved convergence guarantees and acceleration. Temporal difference learning and residual gradient methods are the most widely used temporal difference based learning algorithms. We provide experimental results showing the improved performance of our accelerated gradient td methods.

The proximalproximal gradient algorithm ting kei pong august 23, 20 abstract we consider the problem of minimizing a convex objective which is the sum of a smooth part, with lipschitz continuous gradient, and a nonsmooth part. Linkage effects and analysis of finite sample errors in the. The markov sampling convergence analysis is presented in. Section 3 introduces the proximal gradient method and the convexconcave saddlepoint formulation of nonsmooth convex optimization. B liu, j liu, m ghavamzadeh, s mahadevan, m petrik. Uncertainty in arti cial intelligence, pages 5045, amsterdam, netherlands, 2015. Check the gradients using finite differences stack overflow. The results of our theoretical analysis imply that the gtd family of algorithms are comparable and may indeed be preferred over existing least squares td methods for offpolicy learning, due to their linear complexity. The ones marked may be different from the article in the profile. Preliminary experimental results demonstrate the bene.

Works that managed to obtain concentration bounds for online temporal difference td methods analyzed modified versions of them. Case control panels of cases and controls are generated from 120 chromosomes. Stochastic proximal algorithms for auc maximization michael natole jr. Convex analysis and monotone operator theory in hilbert. Td 0 is one of the most commonly used algorithms in reinforcement learning. Finite sample analysis of the gtd policy evaluation. On generalized bellman equations and temporaldifference. In this paper, our analysis of critic step is focused on td 0 algorithm with linear statevalue function approximation under the in.

Finite sample analyses for td0 with function approximation. Tao sun han shen tianyi chen dongsheng li february 21. We consider offpolicy temporaldifference td learning in discounted markov decision processes, where the goal is to evaluate a policy in a modelfree way by using observations of a state process generated without executing the policy. Recall rg xty x, hence proximal gradient update is. This thesis presents a general framework for firstorder temporal difference learning algorithms with an indepth theoretical analysis. Request pdf finitesample analysis of proximal gradient td algorithms in this paper, we show for the first time how gradient td gtd reinforcement learning methods can be formally derived as. Adaptive temporal difference learning with linear function. This is also called forwardbackward splitting, with the. Algorithms for firstorder sparse reinforcement learning core. Pdf finite sample analysis of twotimescale stochastic.

Gradient based td gtd algorithms including gtd and gtd2 proposed by sutton et al. Marek petrik, ronny luss, interpretable policies for dynamic product recommendations, uncertainty in arti. Conference on uncertainty in arti cial intelligence, 2015. Finite sample analysis of proximal gradient algorithms. In this work, we develop a novel recipe for their finite sample analysis. Designing a true stochastic gradient unconditionally stable temporal difference td method with. In proceedings of the 28th international conference on machine learning, pages 11771184, 2011. Previous analyses of this class of algorithms use stochastic approximation techniques to prove asymptotic convergence, and no finitesample analysis had been attempted. Try the new true gradient rl methods gradient td and proximal gradient td developed by maei 2011 and mahadevan 2015 et al. Nov 2015 our paper uncorrelated group lasso is accepted by aaai2016.

We then use the techniques applied in the analysis of the stochastic gradient methods to propose a uni. Reinforcement learning rl is a modelfree framework for solving optimal control problems stated as markov decision processes mdps puterman, 1994. Finitesample analysis of proximal gradient td algorithms. Finite sample analysis of lstd with random projections and. Finite sample analysis of proximal gradient td algorithms. Bo liu, ji liu, mohammad ghavamzadeh, sridhar mahadevan, marek petrik winner of the facebook best student paper award. Dynamic programming algorithms policy iteration start with an arbitrary policy.

Stochastic proximal algorithms for auc maximization. Proximal gradient temporal difference learning algorithms bo liu, ji liu, mohammad ghavamzadeh, sridhar mahadevan, marek petrik. Proximal gradient methods are a generalized form of projection used to solve nondifferentiable convex optimization problems many interesting problems can be formulated as convex optimization problems of form. We show how gradient td gtd reinforcement learning methods can be formally derived, not by starting from their original objective functions, as. Finitesample analysis of proximal gradient td algorithms proceedings of the 31th conference on uncertainty in artificial intelligence uai, 2015. Request pdf finitesample analysis of proximal gradient td algorithms in this paper, we show for the first time how gradient td gtd reinforcement learning methods can. The algorithm and analysis are based on a reduction of the control of mdps to expert prediction problems evendar et al. Previous analyses of this class of algorithms use ode techniques to show their asymptotic convergence, and to the best of our knowledge, no finite sample. Theorem2 finitesample bound on convergence of sarsa constant stepsize. Works that managed to obtain concentration bounds for online temporal difference td methods analyzed modified versions of them, carefully crafted. Convergent tree backup and retrace with function approximation ahmed touati1 2 pierreluc bacon3 doina precup3 4 pascal vincent1 2 4 abstract.

The effect of finite sample size on power estimation is measured by comparing power estimates at genotyped snps and untyped snps based on simulation over a finite data set. Inspired by various applications, we focus on the case when the nonsmooth part is a composition of a proper closed. Despite this, there is no existing finite sample analysis for td0 with function approximation, even for the linear case. A general gradient algorithm for temporaldi erence prediction learning with eligibility traces. Finitesample analysis of proximal gradient td algorithms 31th conference on uncertainty in artificial intelligence may 1, 2015 facebook best student. One such example is regularization also known as lasso of the form. This enables us to use a limitedmemory sr1 method similar to lbfgs. Finitesample analysis for sarsa and qlearning with. Nonasymptotic analysis for the gradient td a variant of the original td has been first studied in. We also propose an accelerated algorithm, called gtd2mp, that uses proximal mirror maps to yield improved convergence rate. The main contribution of the thesis is the development and design of a family of firstorder regularized temporaldifference td algorithms using stochastic approximation and stochastic optimization. For example, this has been established for the class of forwardbackward algorithms with added noise rosasco et al. Below every paper are top 100 mostoccuring words in that paper and their color is based on lda topic model with k 7.

Convergence analysis of ro td is presented in section 5. Sep 03, 2017 motivated by the widespread use of temporaldifference td and qlearning algorithms in reinforcement learning, this paper studies a class of biased stochastic approximation sa procedures under a mild ergodiclike assumption on the underlying stochastic noise sequence. Twotimescale stochastic approximation sa algorithms are widely used in reinforcement learning rl. In contrast to the standard td learning, targetbased td algorithms. Furthermore, this work assumes that the objective function is composed. Reinforcement learning is one of three basic machine learning paradigms, alongside supervised learning and unsupervised learning.

An accelerated algorithm is also proposed, namely gtd2mp, which use proximal. Existing convergence rates for temporal difference td methods apply only to somewhat modified versions, e. In this paper, we show that the tree backup and retrace algorithms are unstable with linear function approximation, both in theory and with specific examples. In all cases, we give finite sample complexity bounds for our algorithms to recover such winners. Qiang liu, jian peng, alexander ihler, johnfisher iii 514 afinite population likelihood ratiotest ofthe sharp nullhypothesis for compilers. Proceedings of the thirtyfirst conference on uncertainty in artificial intelligence uai2015, pp. Proximal gradient temporal difference learning algorithms. Liu b, liu j, ghavamzadeh m, mahadevan s and petrik m finite sample analysis of proximal gradient td algorithms proceedings of the thirtyfirst conference on uncertainty in artificial intelligence, 5045. Algorithms for firstorder sparse reinforcement learning.

In proceedings of the thirtyfirst conference on uncertainty in arti. Finite sample analysis of lstd with random projections and eligibility traces haifang li1, yingce xia2 and wensheng zhang1 1 institute of automation, chinese academy of sciences, beijing, china 2 university of science and technology of china, hefei, anhui, china haifang. Pdf finite sample analysis for td0 with linear function. Their iterates have two parts that are updated using distinct stepsizes. The use of target networks has been a popular and key component of recent deep qlearning algorithms for reinforcement learning, yet little is known from the theory side. It was discovered more than two decades ago that the original td method was unstable in many off. Reinforcement learning rl is an area of machine learning concerned with how software agents ought to take actions in an environment so as to maximize some notion of cumulative reward. Using this, we provide a concentration bound, which is the first such result for a twotimescale sa. Briefly, the algorithm follows the standard proximal gradient method, but allows a scaled prox. This technique for estimating power is common practice as in the methods of 8, 16.

Finitesample analysis for sarsa and qlearning with linear function approximation shaofeng zou1 tengyu xu 2yingbin liang abstract though the convergence of major reinforcement learning algorithms has been extensively studied. Proximal gradient forward backward splitting methods for learning is an area of research in optimization and statistical learning theory which studies algorithms for a general class of convex regularization problems where the regularization penalty may not be differentiable. Despite this, there is no existing finite sample analysis for td 0 with function approximation, even for the linear case. Finitesample analysis of lassotd gorithmic work on adding 1penalties to the td loth et al. This cited by count includes citations to the following articles in scholar.