We show that the lambda-return target used in the TD(lambda) family of algorithms is the maximum likelihood estimator for a specific model of how the variance of an n-step return estimate increases with n. We introduce the gamma-return estimator, an alternative target based on a more accurate model of variance, which defines the TD_gamma family of complex-backup temporal difference learning algorithms. We derive TD_gamma, the gamma-return equivalent of the original TD(lambda) algorithm, which eliminates the lambda parameter but can only perform updates at the end of an episode and requires time and space proportional to the episode length. We then derive a second algorithm, TD_gamma(C), with a capacity parameter C. TD_gamma(C) requires C times more time and memory than TD(lambda) and is incremental and online. We show that TD_gamma outperforms TD(lambda) for any setting of lambda on 4 out of 5 benchmark domains, and that TD_gamma(C) performs as well as or better than TD_gamma for intermediate settings of C.

We present theoretical and empirical results for a framework that combines the benefits of apprenticeship and autonomous reinforcement learning. Our approach modifies an existing apprenticeship learning framework that relies on teacher demonstrations and does not necessarily explore the environment. The first change is replacing previously used Mistake Bound model learners with a recently proposed framework that melds the KWIK and Mistake Bound supervised learning protocols. The second change is introducing a communication of expected utility from the student to the teacher. The resulting system only uses teacher traces when the agent needs to learn concepts it cannot efficiently learn on its own.

Off-policy learning, the ability for an agent to learn about a policy other than the one it is following, is a key element of Reinforcement Learning, and in recent years there has been much work on developing Temporal Different (TD) algorithms that are guaranteed to converge under off-policy sampling. It has remained an open question, however, whether anything can be said a priori about the quality of the TD solution when off-policy sampling is employed with function approximation. In general the answer is no: for arbitrary off-policy sampling the error of the TD solution can be unboundedly large, even when the approximator can represent the true value function well. In this paper we propose a novel approach to address this problem: we show that by considering a certain convex subset of off-policy distributions we can indeed provide guarantees as to the solution quality similar to the on-policy case. Furthermore, we show that we can efficiently project on to this convex set using only samples generated from the system. The end result is a novel TD algorithm that has approximation guarantees even in the case of off-policy sampling and which empirically outperforms existing TD methods.

We present a novel class of actor-critic algorithms for actors consisting of sets of interacting modules. We present, analyze theoretically, and empirically evaluate an update rule for each module, which requires only local information: the module's input, output, and the TD error broadcast by a critic. Such updates are necessary when computation of compatible features becomes prohibitively difficult and are also desirable to increase the biological plausibility of reinforcement learning methods.

Skill discovery algorithms in reinforcement learning typically identify single states or regions in state space that correspond to task-specific subgoals. However, such methods do not directly address the question of how many distinct skills are appropriate for solving the tasks that the agent faces. This can be highly inefficient when many identified subgoals correspond to the same underlying skill, but are all used individually as skill goals. Furthermore, skills created in this manner are often only transferable to tasks that share identical state spaces, since corresponding subgoals across tasks are not merged into a single skill goal. We show that these problems can be overcome by clustering subgoal data defined in an agent-space and using the resulting clusters as templates for skill termination conditions. Clustering via a Dirichlet process mixture model is used to discover a minimal, sufficient collection of portable skills.

Transfer reinforcement learning (RL) methods leverage on the experience collected on a set of source tasks to speed-up RL algorithms. A simple and effective approach is to transfer samples from source tasks and include them in the training set used to solve a target task. In this paper, we investigate the theoretical properties of this transfer method and we introduce novel algorithms adapting the transfer process on the basis of the similarity between source and target tasks. Finally, we report illustrative experimental results in a continuous chain problem.

In this paper, we consider the problem of policy evaluation for continuous-state systems. We present a non-parametric approach to policy evaluation, which uses kernel density estimation to represent the system. The true form of the value function for this model can be determined, and can be computed using Galerkin's method. Furthermore, we also present a unified view of several well-known policy evaluation methods. In particular, we show that the same Galerkin method can be used to derive Least-Squares Temporal Difference learning, Kernelized Temporal Difference learning, and a discrete-state Dynamic Programming solution, as well as our proposed method. In a numerical evaluation of these algorithms, the proposed approach performed better than the other methods.

Kernel-based reinforcement-learning (KBRL) is a method for learning a decision policy from a set of sample transitions which stands out for its strong theoretical guarantees. However, the size of the approximator grows with the number of transitions, which makes the approach impractical for large problems. In this paper we introduce a novel algorithm to improve the scalability of KBRL. We resort to a special decomposition of a transition matrix, called stochastic factorization, to fix the size of the approximator while at the same time incorporating all the information contained in the data. The resulting algorithm, kernel-based stochastic factorization (KBSF), is much faster but still converges to a unique solution. We derive a theoretical upper bound for the distance between the value functions computed by KBRL and KBSF. The effectiveness of our method is illustrated with computational experiments on four reinforcement-learning problems, including a difficult task in which the goal is to learn a neurostimulation policy to suppress the occurrence of seizures in epileptic rat brains. We empirically demonstrate that the proposed approach is able to compress the information contained in KBRL's model. Also, on the tasks studied, KBSF outperforms two of the most prominent reinforcement-learning algorithms, namely least-squares policy iteration and fitted Q-iteration.

Policy gradient is a useful model-free reinforcement learning approach, but it tends to suffer from instability of gradient estimates. In this paper, we analyze and improve the stability of policy gradient methods. We first prove that the variance ofgradient estimates in the PGPE (policy gradients with parameter-based exploration) method is smaller than that of the classical REINFORCE method under a mild assumption. We then derive the optimal baseline for PGPE, which contributes to further reducing the variance. We also theoretically show that PGPE with the optimal baseline is more preferable than REINFORCE with the optimal baseline in terms of the variance of gradient estimates. Finally, we demonstrate the usefulness of the improved PGPE method through experiments.

Many practitioners of reinforcement learning problems have observed that oftentimes the performance of the agent reaches very close to the optimal performance even though the estimated (action-)value function is still far from the optimal one. The goal of this paper is to explain and formalize this phenomenon by introducing the concept of the action-gap regularity. As a typical result, we prove that for an agent following the greedy policy \(\hat{\pi}\) with respect to an action-value function \(\hat{Q}\), the performance loss \(E[V^*(X) - V^{\hat{X}} (X)]\) is upper bounded by \(O(|| \hat{Q} - Q^*||_\infty^{1+\zeta}\)), in which \(\zeta >= 0\) is the parameter quantifying the action-gap regularity. For \(\zeta > 0\), our results indicate smaller performance loss compared to what previous analyses had suggested. Finally, we show how this regularity affects the performance of the family of approximate value iteration algorithms.