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.

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 generalise the problem of inverse reinforcement learning to multiple tasks, from multiple demonstrations. Each one may represent one expert trying to solve a different task, or as different experts trying to solve the same task. Our main contribution is to formalise the problem as statistical preference elicitation, via a number of structured priors, whose form captures our biases about the relatedness of different tasks or expert policies. In doing so, we introduce a prior on policy optimality, which is more natural to specify. We show that our framework allows us not only to learn to efficiently from multiple experts but to also effectively differentiate between the goals of each. Possible applications include analysing the intrinsic motivations of subjects in behavioural experiments and learning from multiple teachers.

In the Bayesian approach to sequential decision making, exact calculation of the (subjective) utility is intractable. This extends to most special cases of interest, such as reinforcement learning problems. While utility bounds are known to exist for this problem, so far none of them were particularly tight. In this paper, we show how to efficiently calculate a lower bound, which corresponds to the utility of a near-optimal memoryless policy for the decision problem, which is generally different from both the Bayes-optimal policy and the policy which is optimal for the expected MDP under the current belief. We then show how these can be applied to obtain robust exploration policies in a Bayesian reinforcement learning setting.

Suppose an agent builds a policy that satisfactorily solves a decision problem; suppose further that some aspects of this policy are abstracted and used as starting point in a new, different decision problem. How can the agent accrue the benefits of the abstract policy in the new concrete problem? In this paper we propose a framework for simultaneous reinforcement learning, where the abstract policy helps start up the policy for the concrete problem, and both policies are refined through exploration. We report experiments that demonstrate that our framework is effective in speeding up policy construction for practical problems.

The exploration-exploitation trade-off is among the central challenges of reinforcement learning. The optimal Bayesian solution is intractable in general. This paper studies to what extent analytic statements about optimal learning are possible if all beliefs are Gaussian processes. A first order approximation of learning of both loss and dynamics, for nonlinear, time-varying systems in continuous time and space, subject to a relatively weak restriction on the dynamics, is described by an infinite-dimensional partial differential equation. An approximate finite-dimensional projection gives an impression for how this result may be helpful.

We consider the discrete-time infinite-horizon optimal control problem formalized by Markov Decision Processes. We revisit the work of Bertsekas and Ioffe, that introduced $\lambda$ Policy Iteration, a family of algorithms parameterized by $\lambda$ that generalizes the standard algorithms Value Iteration and Policy Iteration, and has some deep connections with the Temporal Differences algorithm TD($\lambda$) described by Sutton and Barto. We deepen the original theory developped by the authors by providing convergence rate bounds which generalize standard bounds for Value Iteration described for instance by Puterman. Then, the main contribution of this paper is to develop the theory of this algorithm when it is used in an approximate form and show that this is sound. Doing so, we extend and unify the separate analyses developped by Munos for Approximate Value Iteration and Approximate Policy Iteration. Eventually, we revisit the use of this algorithm in the training of a Tetris playing controller as originally done by Bertsekas and Ioffe. We provide an original performance bound that can be applied to such an undiscounted control problem. Our empirical results are different from those of Bertsekas and Ioffe (which were originally qualified as "paradoxical" and "intriguing"), and much more conform to what one would expect from a learning experiment. We discuss the possible reason for such a difference.

The creation of effective autonomous agents (bots) for combat scenarios has long been a goal of the gaming industry. However, a secondary consideration is whether the autonomous bots behave like human players; this is especially important for simulation/training applications which aim to instruct participants in real-world tasks. Bots often compensate for a lack of combat acumen with advantages such as accurate targeting, predefined navigational networks, and perfect world knowledge, which makes them challenging but often predictable opponents. In this paper, we examine the problem of teaching a bot to play like a human in first-person shooter game combat scenarios. Our bot learns attack, exploration and targeting policies from data collected from expert human player demonstrations in Unreal Tournament. We hypothesize that one key difference between human players and autonomous bots lies in the relative valuation of game states. To capture the internal model used by expert human players to evaluate the benefits of different actions, we use inverse reinforcement learning to learn rewards for different game states. We report the results of a human subjects' study evaluating the performance of bot policies learned from human demonstration against a set of standard bot policies. Our study reveals that human players found our bots to be significantly more human-like than the standard bots during play. Our technique represents a promising stepping-stone toward addressing challenges such as the Bot Turing Test (the CIG Bot 2K Competition).

In this work, we look at the challenge of learning in an action game,Infinite Mario. Learning to play an action game can be divided intotwo distinct but related problems, learning an object-relatedbehavior and selecting a primitive action. We propose a framework that allows for the use of reinforcement learning for both ofthese problems. We present promising results in some instances of thegame and identify some problems that might affect learning.

We study an approach to policy selection for large relational Markov Decision Processes (MDPs). We consider a variant of approximate policy iteration (API) that replaces the usual value-function learning step with a learning step in policy space. This is advantageous in domains where good policies are easier to represent and learn than the corresponding value functions, which is often the case for the relational MDPs we are interested in. In order to apply API to such problems, we introduce a relational policy language and corresponding learner. In addition, we introduce a new bootstrapping routine for goal-based planning domains, based on random walks. Such bootstrapping is necessary for many large relational MDPs, where reward is extremely sparse, as API is ineffective in such domains when initialized with an uninformed policy. Our experiments show that the resulting system is able to find good policies for a number of classical planning domains and their stochastic variants by solving them as extremely large relational MDPs. The experiments also point to some limitations of our approach, suggesting future work.