Online Convex Optimization for Sequential Decision Processes and Extensive-Form Games

Regret minimization is a powerful tool for solving large-scale extensive-form games. State-of-the-art methods rely on minimizing regret locally at each decision point. In this work we derive a new framework for regret minimization on sequential decision problems and extensive-form games with general compact convex sets at each decision point and general convex losses, as opposed to prior work which has been for simplex decision points and linear losses. We call our framework laminar regret decomposition. It generalizes the CFR algorithm to this more general setting. Furthermore, our framework enables a new proof of CFR even in the known setting, which is derived from a perspective of decomposing polytope regret, thereby leading to an arguably simpler interpretation of the algorithm. Our generalization to convex compact sets and convex losses allows us to develop new algorithms for several problems: regularized sequential decision making, regularized Nash equilibria in extensive-form games, and computing approximate extensive-form perfect equilibria. Our generalization also leads to the first regret-minimization algorithm for computing reduced-normal-form quantal response equilibria based on minimizing local regrets. Experiments show that our framework leads to algorithms that scale at a rate comparable to the fastest variants of counterfactual regret minimization for computing Nash equilibrium, and therefore our approach leads to the first algorithm for computing quantal response equilibria in extremely large games. Finally we show that our framework enables a new kind of scalable opponent exploitation approach

Imperfect-Recall Abstractions with Bounds in Games

Imperfect-recall abstraction has emerged as the leading paradigm for practical large-scale equilibrium computation in incomplete-information games. However, imperfect-recall abstractions are poorly understood, and only weak algorithm-specific guarantees on solution quality are known. In this paper, we show the first general, algorithm-agnostic, solution quality guarantees for Nash equilibria and approximate self-trembling equilibria computed in imperfect-recall abstractions, when implemented in the original (perfect-recall) game. Our results are for a class of games that generalizes the only previously known class of imperfect-recall abstractions where any results had been obtained. Further, our analysis is tighter in two ways, each of which can lead to an exponential reduction in the solution quality error bound. We then show that for extensive-form games that satisfy certain properties, the problem of computing a bound-minimizing abstraction for a single level of the game reduces to a clustering problem, where the increase in our bound is the distance function. This reduction leads to the first imperfect-recall abstraction algorithm with solution quality bounds. We proceed to show a divide in the class of abstraction problems. If payoffs are at the same scale at all information sets considered for abstraction, the input forms a metric space. Conversely, if this condition is not satisfied, we show that the input does not form a metric space. Finally, we use these results to experimentally investigate the quality of our bound for single-level abstraction

Solving Uncertain MDPs with Objectives that are Separable over Instantiations of Model Uncertainty

National Research Foundation (NRF) Singapore under SMART and Future Mobilit

Sampling based approaches for minimizing regret in uncertain Markov Decision Problems (MDPs)

National Research Foundation (NRF) Singapore under Singapore-MIT Alliance for Research and Technology (SMART) Center for Future Mobilit