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We formulate the novel class of contextual games, a type of repeated games driven by contextual information at each round. By means of kernel-based regularity assumptions, we model the correlation between different contexts and game…

In game theory, mechanism design is concerned with the design of incentives so that a desired outcome of the game can be achieved. In this paper, we study the design of incentives so that a desirable equilibrium is obtained, for instance,…

We study estimation and inference using data collected by reinforcement learning (RL) algorithms. These algorithms adaptively experiment by interacting with individual units over multiple stages, updating their strategies based on past…

In this paper, we propose a provably convergent and practical framework for multi-objective reinforcement learning with max-min criterion. From a game-theoretic perspective, we reformulate max-min multi-objective reinforcement learning as a…

Games with continuous strategy sets arise in several machine learning problems (e.g. adversarial learning). For such games, simple no-regret learning algorithms exist in several cases and ensure convergence to coarse correlated equilibria…

We introduce a new algorithm for multi-objective reinforcement learning (MORL) with linear preferences, with the goal of enabling few-shot adaptation to new tasks. In MORL, the aim is to learn policies over multiple competing objectives…

We obtain global, non-asymptotic convergence guarantees for independent learning algorithms in competitive reinforcement learning settings with two agents (i.e., zero-sum stochastic games). We consider an episodic setting where in each…

In this paper, we establish a subgame perfect equilibrium reinforcement learning (SPERL) framework for time-inconsistent (TIC) problems. In the context of RL, TIC problems are known to face two main challenges: the non-existence of natural…

We consider graph games of infinite duration with winning conditions in parameterized linear temporal logic, where the temporal operators are equipped with variables for time bounds. In model checking such specifications were introduced as…

In this paper, we consider the problem of optimization and learning for constrained and multi-objective Markov decision processes, for both discounted rewards and expected average rewards. We formulate the problems as zero-sum games where…

In multi-agent tasks, the central challenge lies in the dynamic adaptation of strategies. However, directly conditioning on opponents' strategies is intractable in the prevalent deep reinforcement learning paradigm due to a fundamental…

We provide a unifying view of a large family of previous imitation learning algorithms through the lens of moment matching. At its core, our classification scheme is based on whether the learner attempts to match (1) reward or (2)…

We study mean field games with scalar It{\^o}-type dynamics and costs that are submodular with respect to a suitable order relation on the state and measure space. The submodularity assumption has a number of interesting consequences.…

Finite mixture models are an important tool in the statistical analysis of data, for example in data clustering. The optimal parameters of a mixture model are usually computed by maximizing the log-likelihood functional via the…

Although well-established in general reinforcement learning (RL), value-based methods are rarely explored in constrained RL (CRL) for their incapability of finding policies that can randomize among multiple actions. To apply value-based…

Empirical risk minimization (ERM) is ubiquitous in machine learning and underlies most supervised learning methods. While there has been a large body of work on algorithms for various ERM problems, the exact computational complexity of ERM…

This article explores the optimisation of trading strategies in Constant Function Market Makers (CFMMs) and centralised exchanges. We develop a model that accounts for the interaction between these two markets, estimating the conditional…

We consider an N-player hierarchical game in which the i-th player's objective comprises of an expectation-valued term, parametrized by rival decisions, and a hierarchical term. Such a framework allows for capturing a broad range of…

Recent techniques based on Mean Field Games (MFGs) allow the scalable analysis of multi-player games with many similar, rational agents. However, standard MFGs remain limited to homogeneous players that weakly influence each other, and…

We study a portfolio optimization problem for competitive agents with CRRA utilities and a common finite time horizon. The utility of an agent depends not only on her absolute wealth and consumption but also on her relative wealth and…