We propose a new approach to reinforcement learning for control problems which combines value-function approximation with linear architectures and approximate policy iteration.

Reinforcement learning aims to determine an optimal control policy from interaction with a system or from observations gathered from a system. In batch mode, it can be achieved by approximating the so-called Q-function based on a set of four-tuples (xt,ut,rt,xt+1) where xt denotes the system state at time t, ut the control action taken, rt the instantaneous reward obtained and xt+1 the successor state of the system, and by determining the control policy from this Q-function. The Q-function approximation may be obtained from the limit of a sequence of (batch mode) supervised learning problems. Within this framework we describe the use of several classical tree-based supervised learning methods (CART, Kd-tree, tree bagging) and two newly proposed ensemble algorithms, namely extremely and totally randomized trees. We study their performances on several examples and find that the ensemble methods based on regression trees perform well in extracting relevant information about the optimal control policy from sets of four-tuples. In particular, the totally randomized trees give good results while ensuring the convergence of the sequence, whereas by relaxing the convergence constraint even better accuracy results are provided by the extremely randomized trees.

This paper introduces a novel spectral framework for solving Markov decision processes (MDPs) by jointly learning representations and optimal policies. The major components of the framework described in this paper include: (i) A general scheme for constructing representations or basis functions by diagonalizing symmetric diffusion operators (ii) A specific instantiation of this approach where global basis functions called proto-value functions (PVFs) are formed using the eigenvectors of the graph Laplacian on an undirected graph formed from state transitions induced by the MDP (iii) A three-phased procedure called representation policy iteration comprising of a sample collection phase, a representation learning phase that constructs basis functions from samples, and a final parameter estimation phase that determines an (approximately) optimal policy within the (linear) subspace spanned by the (current) basis functions. (iv) A specific instantiation of the RPI framework using least-squares policy iteration (LSPI) as the parameter estimation method (v) Several strategies for scaling the proposed approach to large discrete and continuous state spaces, including the Nyström extension for out-of-sample interpolation of eigenfunctions, and the use of Kronecker sum factorization to construct compact eigenfunctions in product spaces such as factored MDPs (vi) Finally, a series of illustrative discrete and continuous control tasks, which both illustrate the concepts and provide a benchmark for evaluating the proposed approach. Many challenges remain to be addressed in scaling the proposed framework to large MDPs, and several elaboration of the proposed framework are briefly summarized at the end.

We present a novel Bayesian approach to the problem of value function estimation in continuous state spaces. We de ne a probabilistic generative model for the value function by imposing a Gaussian prior over value functions and assuming a Gaussian noise model.

Relational reinforcement learning is a Q-learning technique for relational state-action spaces. It aims to enable agents to learn how to act in an environment that has no natural representation as a tuple of constants. In this case, the learning algorithm used to approximate the mapping between state-action pairs and their so called Q(uality)-value has to be not only very reliable, but it also has to be able to handle the relational representation of state-action pairs. In this paper we investigate...

The reinforcement learning paradigm is a popular way to address problems that have only limited environmental feedback, rather than correctly labeled examples, as is common in other machine learning contexts. While significant progress has been made to improve learning in a single task, the idea of transfer learning has only recently been applied to reinforcement learning tasks. The core idea of transfer is that experience gained in learning to perform one task can help improve learning performance in a related, but different, task. In this article we present a framework that classifies transfer learning methods in terms of their capabilities and goals, and then use it to survey the existing literature, as well as to suggest future directions for transfer learning work.

We incorporate statistical confidence intervals in both the multi-armed bandit and the reinforcement learning problems. In the bandit problem we show that given n arms, it suffices to pull the arms a total of O ) log(1/d) times to find an e-optimal arm with probability of at least 1-d. This bound matches the lower bound of Mannor and Tsitsiklis (2004) up to constants. We also devise action elimination procedures in reinforcement learning algorithms. We describe a framework that is based on learning the confidence interval around the value function or the Q-function and eliminating actions that are not optimal (with high probability). We provide a model-based and a model-free variants of the elimination method. We further derive stopping conditions guaranteeing that the learned policy is approximately optimal with high probability. Simulations demonstrate a considerable speedup and added robustness over e-greedy Q-learning.

We consider a variant of Q-learning in continuous state spaces under the total expected discounted cost criterion combined with local function approximation methods. Provided that the function approximator satisfies certain interpolation properties, the resulting algorithm is shown to converge with probability one. The limit function is shown to satisfy a fixed point equation of the Bellman type, where the fixed point operator depends on the stationary distribution of the exploration policy and the function approximation method. The basic algorithm is extended in several ways. In particular, a variant of the algorithm is obtained that is shown to converge in probability to the optimal Q function. Preliminary computer simulations are presented that confirm the validity of the approach.

We propose a new approach to reinforcement learning which combines least squares function approximation with policy iteration. Our method is model-free and completely off policy. We are motivated by the least squares temporal difference learning algorithm (LSTD), which is known for its efficient use of sample experiences compared to pure temporal difference algorithms. LSTD is ideal for prediction problems, however it heretofore has not had a straightforward application to control problems.

Abstract. CBR is one of the techniques that can be applied to the task of approximating a function over high-dimensional, continuous spaces. In Reinforcement Learning systems a learning agent is faced with the problem of assessing the desirability of the state it finds itself in. If the state space is very large and/or continuous the availability of a suitable mechanism to approximate a value function – which estimates the value of single states – is of crucial importance. In this paper, we investigate the use of case-based methods to realise that task. The approach we take is evaluated in a case study in robotic soccer simulation. 1