We provide a theoretical framework for analyzing basis function construction for linear value function approximation in Markov Decision Processes (MDPs). We show that important existing methods, such as Krylov bases and Bellman-error-based methods are a special case of the general framework we develop. We provide a general algorithmic framework for computing basis function refinements which “respect” the dynamics of the environment, and we derive approximation error bounds that apply for any algorithm respecting this general framework. We also show how, using ideas related to bisimulation metrics, one can translate basis refinement into a process of finding “prototypes” that are diverse enough to represent the given MDP.

Existing inverse reinforcement learning (IRL) algorithms have assumed each expert’s demonstrated trajectory to be produced by only a single reward function. This paper presents a novel generalization of the IRL problem that allows each trajectory to be generated by multiple locally consistent reward functions, hence catering to more realistic and complex experts’ behaviors. Solving our generalized IRL problem thus involves not only learning these reward functions but also the stochastic transitions between them at any state (including unvisited states). By representing our IRL problem with a probabilistic graphical model, an expectation-maximization (EM) algorithm can be devised to iteratively learn the different reward functions and the stochastic transitions between them in order to jointly improve the likelihood of the expert’s demonstrated trajectories. As a result, the most likely partition of a trajectory into segments that are generated from different locally consistent reward functions selected by EM can be derived. Empirical evaluation on synthetic and real-world datasets shows that our IRL algorithm outperforms the state-of-the-art EM clustering with maximum likelihood IRL, which is, interestingly, a reduced variant of our approach.

Recently, there has been significant progress in understanding reinforcement learning in discounted infinite-horizon Markov decision processes (MDPs) by deriving tight sample complexity bounds. However, in many real-world applications, an interactive learning agent operates for a fixed or bounded period of time, for example tutoring students for exams or handling customer service requests. Such scenarios can often be better treated as episodic fixed-horizon MDPs, for which only looser bounds on the sample complexity exist. A natural notion of sample complexity in this setting is the number of episodes required to guarantee a certain performance with high probability (PAC guarantee). In this paper, we derive an upper PAC bound of order O(|S|²|A|H² log(1/δ)/ɛ²) and a lower PAC bound Ω(|S||A|H² log(1/(δ+c))/ɛ²) (ignoring log-terms) that match up to log-terms and an additional linear dependency on the number of states |S|. The lower bound is the first of its kind for this setting. Our upper bound leverages Bernstein's inequality to improve on previous bounds for episodic finite-horizon MDPs which have a time-horizon dependency of at least H³.

We propose the Ω-return as an alternative to the λ-return currently used by the TD(λ) family of algorithms. The benefit of the Ω-return is that it accounts for the correlation of different length returns. Because it is difficult to compute exactly, we suggest one way of approximating the Ω-return. We provide empirical studies that suggest that it is superior to the λ-return and γ-return for a variety of problems.

Bounded rationality, that is, decision-making and planning under resource limitations, is widely regarded as an important open problem in artificial intelligence, reinforcement learning, computational neuroscience and economics. This paper offers a consolidated presentation of a theory of bounded rationality based on information-theoretic ideas. We provide a conceptual justification for using the free energy functional as the objective function for characterizing bounded-rational decisions. This functional possesses three crucial properties: it controls the size of the solution space; it has Monte Carlo planners that are exact, yet bypass the need for exhaustive search; and it captures model uncertainty arising from lack of evidence or from interacting with other agents having unknown intentions. We discuss the single-step decision-making case, and show how to extend it to sequential decisions using equivalence transformations. This extension yields a very general class of decision problems that encompass classical decision rules (e.g.

We consider the off-policy evaluation problem in Markov decision processes with function approximation. We propose a generalization of the recently introduced \emph{emphatic temporal differences} (ETD) algorithm \citep{SuttonMW15}, which encompasses the original ETD($\lambda$), as well as several other off-policy evaluation algorithms as special cases. We call this framework \ETD, where our introduced parameter $\beta$ controls the decay rate of an importance-sampling term. We study conditions under which the projected fixed-point equation underlying \ETD\ involves a contraction operator, allowing us to present the first asymptotic error bounds (bias) for \ETD. Our results show that the original ETD algorithm always involves a contraction operator, and its bias is bounded. Moreover, by controlling $\beta$, our proposed generalization allows trading-off bias for variance reduction, thereby achieving a lower total error.

We introduce a model-free algorithm for learning in Markov decision processes with parameterized actions-discrete actions with continuous parameters. At each step the agent must select both which action to use and which parameters to use with that action. We introduce the Q-PAMDP algorithm for learning in these domains, show that it converges to a local optimum, and compare it to direct policy search in the goal-scoring and Platform domains.

To identify the location of objects of a particular class, a passive computer vision system generally processes all the regions in an image to finally output few regions. However, we can use structure in the scene to search for objects without processing the entire image. We propose a search technique that sequentially processes image regions such that the regions that are more likely to correspond to the query class object are explored earlier. We frame the problem as a Markov decision process and use an imitation learning algorithm to learn a search strategy. Since structure in the scene is essential for search, we work with indoor scene images as they contain both unary scene context information and object-object context in the scene. We perform experiments on the NYU-depth v2 dataset and show that the unary scene context features alone can achieve a significantly high average precision while processing only 20-25\% of the regions for classes like bed and sofa. By considering object-object context along with the scene context features, the performance is further improved for classes like counter, lamp, pillow and sofa.

Achieving efficient and scalable exploration in complex domains poses a major challenge in reinforcement learning. While Bayesian and PAC-MDP approaches to the exploration problem offer strong formal guarantees, they are often impractical in higher dimensions due to their reliance on enumerating the state-action space. Hence, exploration in complex domains is often performed with simple epsilon-greedy methods. In this paper, we consider the challenging Atari games domain, which requires processing raw pixel inputs and delayed rewards. We evaluate several more sophisticated exploration strategies, including Thompson sampling and Boltzman exploration, and propose a new exploration method based on assigning exploration bonuses from a concurrently learned model of the system dynamics. By parameterizing our learned model with a neural network, we are able to develop a scalable and efficient approach to exploration bonuses that can be applied to tasks with complex, high-dimensional state spaces. In the Atari domain, our method provides the most consistent improvement across a range of games that pose a major challenge for prior methods. In addition to raw game-scores, we also develop an AUC-100 metric for the Atari Learning domain to evaluate the impact of exploration on this benchmark.

This book-length article combines several peer reviewed papers and new material to analyze the issues of ethical artificial intelligence (AI). The behavior of future AI systems can be described by mathematical equations, which are adapted to analyze possible unintended AI behaviors and ways that AI designs can avoid them. This article makes the case for utility-maximizing agents and for avoiding infinite sets in agent definitions. It shows how to avoid agent self-delusion using model-based utility functions and how to avoid agents that corrupt their reward generators (sometimes called "perverse instantiation") using utility functions that evaluate outcomes at one point in time from the perspective of humans at a different point in time. It argues that agents can avoid unintended instrumental actions (sometimes called "basic AI drives" or "instrumental goals") by accurately learning human values. This article defines a self-modeling agent framework and shows how it can avoid problems of resource limits, being predicted by other agents, and inconsistency between the agent's utility function and its definition (one version of this problem is sometimes called "motivated value selection"). This article also discusses how future AI will differ from current AI, the politics of AI, and the ultimate use of AI to help understand the nature of the universe and our place in it.