Optimal solutions to Markov Decision Problems (MDPs) are very sensitive with respect to the state transition probabilities. In many practical problems, the estimation of those probabilities is far from accurate. Hence, estimation errors are limiting factors in applying MDPs to realworld problems. We propose an algorithm for solving finite-state and finite-action MDPs, where the solution is guaranteed to be robust with respect to estimation errors on the state transition probabilities. Our algorithm involves a statistically accurate yet numerically efficient representation of uncertainty, via Kullback-Leibler divergence bounds. The worst-case complexity of the robust algorithm is the same as the original Bellman recursion. Hence, robustness can be added at practically no extra computing cost.

We consider the policy search approach to reinforcement learning. We show that if a "baseline distribution" is given (indicating roughly how often we expect a good policy to visit each state), then we can derive a policy search algorithm that terminates in a finite number of steps, and for which we can provide nontrivial performance guarantees. We also demonstrate this algorithm on several grid-world POMDPs, a planar biped walking robot, and a double-pole balancing problem.

We describe a new approximation algorithm for solving partially observable MDPs. Our bounded policy iteration approach searches through the space of bounded-size, stochastic finite state controllers, combining several advantages of gradient ascent (efficiency, search through restricted controller space) and policy iteration (less vulnerability to local optima).

The so-called "experts algorithms" constitute a methodology for choosing actions repeatedly, when the rewards depend both on the choice of action and on the unknown current state of the environment. An experts algorithm has access to a set of strategies ("experts"), each of which may recommend which action to choose. The algorithm learns how to combine the recommendations of individual experts so that, in the long run, for any fixed sequence of states of the environment, it does as well as the best expert would have done relative to the same sequence. This methodology may not be suitable for situations where the evolution of states of the environment depends on past chosen actions, as is usually the case, for example, in a repeated nonzero-sum game. A new experts algorithm is presented and analyzed in the context of repeated games. It is shown that asymptotically, under certain conditions, it performs as well as the best available expert. This algorithm is quite different from previously proposed experts algorithms. It represents a shift from the paradigms of regret minimization and myopic optimization to consideration of the long-term effect of a player's actions on the opponent's actions or the environment. The importance of this shift is demonstrated by the fact that this algorithm is capable of inducing cooperation in the repeated Prisoner's Dilemma game, whereas previous experts algorithms converge to the suboptimal non-cooperative play.

In large multiagent games, partial observability, coordination, and credit assignment persistently plague attempts to design good learning algorithms. We provide a simple and efficient algorithm that in part uses a linear system to model the world from a single agent's limited perspective, and takes advantage of Kalman filtering to allow an agent to construct a good training signal and learn an effective policy.

Online mechanism design (MD) considers the problem of providing incentives to implement desired system-wide outcomes in systems with self-interested agents that arrive and depart dynamically. Agents can choose to misrepresent their arrival and departure times, in addition to information about their value for different outcomes. We consider the problem of maximizing the total longterm value of the system despite the self-interest of agents. The online MD problem induces a Markov Decision Process (MDP), which when solved can be used to implement optimal policies in a truth-revealing Bayesian-Nash equilibrium.

A mobile robot acting in the world is faced with a large amount of sensory data and uncertainty in its action outcomes. Indeed, almost all interesting sequential decision-making domains involve large state spaces and large, stochastic action sets. We investigate a way to act intelligently as quickly as possible in domains where finding a complete policy would take a hopelessly long time.

Recent research has demonstrated that useful POMDP solutions do not require consideration of the entire belief space. We extend this idea with the notion of temporal abstraction. We present and explore a new reinforcement learning algorithm over grid-points in belief space, which uses macro-actions and Monte Carlo updates of the Q-values. We apply the algorithm to a large scale robot navigation task and demonstrate that with temporal abstraction we can consider an even smaller part of the belief space, we can learn POMDP policies faster, and we can do information gathering more efficiently.

In real world planning problems, time for deliberation is often limited. Anytime planners are well suited for these problems: they find a feasible solution quickly and then continually work on improving it until time runs out. In this paper we propose an anytime heuristic search, ARA*, which tunes its performance bound based on available search time. It starts by finding a suboptimal solution quickly using a loose bound, then tightens the bound progressively as time allows. Given enough time it finds a provably optimal solution. While improving its bound, ARA* reuses previous search efforts and, as a result, is significantly more efficient than other anytime search methods. In addition to our theoretical analysis, we demonstrate the practical utility of ARA* with experiments on a simulated robot kinematic arm and a dynamic path planning problem for an outdoor rover.

Recent developments in grid-based and point-based approximation algorithms for POMDPs have greatly improved the tractability of POMDP planning. These approaches operate on sets of belief points by individually learning a value function for each point. In reality, belief points exist in a highly-structured metric simplex, but current POMDP algorithms do not exploit this property. This paper presents a new metric-tree algorithm which can be used in the context of POMDP planning to sort belief points spatially, and then perform fast value function updates over groups of points. We present results showing that this approach can reduce computation in point-based POMDP algorithms for a wide range of problems.