LSPI with Random Projections

We consider the problem of reinforcement learning in high-dimensional spaces when the number of features is bigger than the number of samples. In particular, we study the least-squares temporal difference (LSTD) learning algorithm when a space of low dimension is generated with a random projection from a high-dimensional space. We provide a thorough theoretical analysis of the LSTD with random projections and derive performance bounds for the resulting algorithm. We also show how the error of LSTD with random projections is propagated through the iterations of a policy iteration algorithm and provide a performance bound for the resulting least-squares policy iteration (LSPI) algorithm

Bellman Error Based Feature Generation using Random Projections on Sparse Spaces

We address the problem of automatic generation of features for value function approximation. Bellman Error Basis Functions (BEBFs) have been shown to improve the error of policy evaluation with function approximation, with a convergence rate similar to that of value iteration. We propose a simple, fast and robust algorithm based on random projections to generate BEBFs for sparse feature spaces. We provide a finite sample analysis of the proposed method, and prove that projections logarithmic in the dimension of the original space are enough to guarantee contraction in the error. Empirical results demonstrate the strength of this method

Intelligent Control of a Sensor-Actuator System via Kernelized Least-Squares Policy Iteration

In this paper a new framework, called Compressive Kernelized Reinforcement Learning (CKRL), for computing near-optimal policies in sequential decision making with uncertainty is proposed via incorporating the non-adaptive data-independent Random Projections and nonparametric Kernelized Least-squares Policy Iteration (KLSPI). Random Projections are a fast, non-adaptive dimensionality reduction framework in which high-dimensionality data is projected onto a random lower-dimension subspace via spherically random rotation and coordination sampling. KLSPI introduce kernel trick into the LSPI framework for Reinforcement Learning, often achieving faster convergence and providing automatic feature selection via various kernel sparsification approaches. In this approach, policies are computed in a low-dimensional subspace generated by projecting the high-dimensional features onto a set of random basis. We first show how Random Projections constitute an efficient sparsification technique and how our method often converges faster than regular LSPI, while at lower computational costs. Theoretical foundation underlying this approach is a fast approximation of Singular Value Decomposition (SVD). Finally, simulation results are exhibited on benchmark MDP domains, which confirm gains both in computation time and in performance in large feature spaces

Finite-Sample Analysis of Least-Squares Policy Iteration

International audienceIn this paper, we report a performance bound for the widely used least-squares policy iteration (LSPI) algorithm. We first consider the problem of policy evaluation in reinforcement learning, that is, learning the value function of a fixed policy, using the least-squares temporal-difference (LSTD) learning method, and report finite-sample analysis for this algorithm. To do so, we first derive a bound on the performance of the LSTD solution evaluated at the states generated by the Markov chain and used by the algorithm to learn an estimate of the value function. This result is general in the sense that no assumption is made on the existence of a stationary distribution for the Markov chain. We then derive generalization bounds in the case when the Markov chain possesses a stationary distribution and is $\beta$-mixing. Finally, we analyze how the error at each policy evaluation step is propagated through the iterations of a policy iteration method, and derive a performance bound for the LSPI algorithm

Policy evaluation with temporal differences: a survey and comparison

Policy evaluation is an essential step in most reinforcement learning approaches. It yields a value function, the quality assessment of states for a given policy, which can be used in a policy improvement step. Since the late 1980s, this research area has been dominated by temporal-difference (TD) methods due to their data-efficiency. However, core issues such as stability guarantees in the off-policy scenario, improved sample efficiency and probabilistic treatment of the uncertainty in the estimates have only been tackled recently, which has led to a large number of new approaches. This paper aims at making these new developments accessible in a concise overview, with foci on underlying cost functions, the off-policy scenario as well as on regularization in high dimensional feature spaces. By presenting the first extensive, systematic comparative evaluations comparing TD, LSTD, LSPE, FPKF, the residual- gradient algorithm, Bellman residual minimization, GTD, GTD2 and TDC, we shed light on the strengths and weaknesses of the methods. Moreover, we present alternative versions of LSTD and LSPE with drastically improved off-policy performance

Representation discovery using a fixed basis in reinforcement learning

A thesis presented for the degree of Doctor of Philosophy, School of Computer Science and Applied Mathematics. University of the Witwatersrand, South Africa. 26 August 2016.In the reinforcement learning paradigm, an agent learns by interacting with its environment. At each state, the agent receives a numerical reward. Its goal is to maximise the discounted sum of future rewards. One way it can do this is through learning a value function; a function which maps states to the discounted sum of future rewards. With an accurate value function and a model of the environment, the agent can take the optimal action in each state. In practice, however, the value function is approximated, and performance depends on the quality of the approximation. Linear function approximation is a commonly used approximation scheme, where the value function is represented as a weighted sum of basis functions or features. In continuous state environments, there are infinitely many such features to choose from, introducing the new problem of feature selection. Existing algorithms such as OMP-TD are slow to converge, scale poorly to high dimensional spaces, and have not been generalised to the online learning case. We introduce heuristic methods for reducing the search space in high dimensions that significantly reduce computational costs and also act as regularisers. We extend these methods and introduce feature regularisation for incremental feature selection in the batch learning case, and show that introducing a smoothness prior is effective with our SSOMP-TD and STOMP-TD algorithms. Finally we generalise OMP-TD and our algorithms to the online case and evaluate them empirically.LG201