Performative prediction is a recently proposed framework where predictions guide decision-making and hence influence future data distributions. Such performative phenomena are ubiquitous in various areas, such as transportation, finance, public policy, and recommendation systems. To date, work on performative prediction has only focused on unconstrained scenarios, neglecting the fact that many realworld learning problems are subject to constraints.

Bandits, Reinforcement Learning

In contrast to the advances in characterizing the sample complexity for solving Markov decision processes (MDPs), the optimal statistical complexity for solving constrained MDPs (CMDPs) remains unknown. We resolve this question by providing minimax upper and lower bounds on the sample complexity for learning near-optimal policies in a discounted CMDP with access to a generative model (simulator). In particular, we design a model-based algorithm that addresses two settings: (i) relaxed feasibility, where small constraint violations are allowed, and (ii) strict feasibility, where the output policy is required to satisfy the constraint.

We consider cooperative multi-agent consensus optimization problems over anundirected network of agents, where only those agents connected by an edgecan directly communicate. The objective is to minimize the sum of agent-specific composite convex functions over agent-specific private conic constraintsets; hence, the optimal consensus decision should lie in the intersection of theseprivate sets. We provide convergence rates in sub-optimality, infeasibility andconsensus violation; examine the effect of underlying network topology on theconvergence rates of the proposed decentralized algorithms; and show how to ex-tend these methods to handle time-varying communication networks.

We exploit the richstructures ofthereformulated problem anddevelopastochastic primal-dual algorithm, SVRPDA-I, to solve the problem efficiently.

Bandits, Reinforcement Learning