This paper analyzes a connection between risk-sensitive and minimax criteria for discrete-time, nite-state Markov Decision Processes (MDPs). We synthesize optimal policies with respect to both criteria, both for nite horizon and discounted in nite horizon problems. A generalized decision-making framework is introduced, leading to stationary risk-sensitive and minimax optimal policies on the in ...

We propose a semidefinite optimization (SDP) model for the class of minimax two-stage stochastic linear optimization problems with risk aversion. The distribution of second-stage random variables belongs to a set of multivariate distributions with known first and second moments. For the minimax stochastic problem with random objective, we provide a tight SDP formulation. The problem with random...

When several agents learn concurrently, the payoff received by an agent is dependent on the behavior of the other agents. As the other agents learn, the reward of one agent becomes non-stationary. This makes learning in multiagent systems more difficult than single-agent learning. A few methods, however, are known to guarantee convergence to equilibrium in the limit in such systems. In this pap...

Since its inception, the modus operandi of multi-task learning (MTL) has been to minimize the task-wise mean of the empirical risks. We introduce a generalized loss-compositional paradigm for MTL that includes a spectrum of formulations as a subfamily. One endpoint of this spectrum is minimax MTL: a new MTL formulation that minimizes the maximum of the tasks’ empirical risks. Via a certain rela...

Monte-Carlo Tree Search (MCTS) has been found to play suboptimally in some tactical domains due to its highly selective search, focusing only on the most promising moves. In order to combine the strategic strength of MCTS and the tactical strength of minimax, MCTSminimax hybrids have been introduced, embedding shallow minimax searches into the MCTS framework. Their results have been promising e...

Agglomerative hierarchical clustering is a popular class of methods for understanding the structure of a dataset. The nature of the clustering depends on the choice of linkage-that is, on how one measures the distance between clusters. In this article we investigate minimax linkage, a recently introduced but little-studied linkage. Minimax linkage is unique in naturally associating a prototype ...

This paper presents an overview of some recent results concerning the emerging theory of minimax LQG control for uncertain systems with a relative entropy constraint uncertainty description. This is an important new robust control system design methodology providing minimax optimal performance in terms of a quadratic cost functional. The paper first considers some standard uncertainty descripti...