We study the convergence of $Q$-learning with linear function approximation. Our key contribution is the introduction of a novel multi-Bellman operator that extends the traditional Bellman operator. By exploring the properties of this operator, we identify conditions under which the projected multi-Bellman operator becomes contractive, providing improved fixed-point guarantees compared to the Bellman operator. To leverage these insights, we propose the multi $Q$-learning algorithm with linear function approximation. We demonstrate that this algorithm converges to the fixed-point of the projected multi-Bellman operator, yielding solutions of arbitrary accuracy. Finally, we validate our approach by applying it to well-known environments, showcasing the effectiveness and applicability of our findings.

We introduce hybrid execution in multi-agent reinforcement learning (MARL), a new paradigm in which agents aim to successfully complete cooperative tasks with arbitrary communication levels at execution time by taking advantage of information-sharing among the agents. Under hybrid execution, the communication level can range from a setting in which no communication is allowed between agents (fully decentralized), to a setting featuring full communication (fully centralized), but the agents do not know beforehand which communication level they will encounter at execution time. To formalize our setting, we define a new class of multi-agent partially observable Markov decision processes (POMDPs) that we name hybrid-POMDPs, which explicitly model a communication process between the agents. We contribute MARO, an approach that makes use of an auto-regressive predictive model, trained in a centralized manner, to estimate missing agents' observations at execution time. We evaluate MARO on standard scenarios and extensions of previous benchmarks tailored to emphasize the negative impact of partial observability in MARL. Experimental results show that our method consistently outperforms relevant baselines, allowing agents to act with faulty communication while successfully exploiting shared information.

We study the interplay between the data distribution and Q-learning-based algorithms with function approximation. We provide a unified theoretical and empirical analysis as to how different properties of the data distribution influence the performance of Q-learning-based algorithms. We connect different lines of research, as well as validate and extend previous results. We start by reviewing theoretical bounds on the performance of approximate dynamic programming algorithms. We then introduce a novel four-state MDP specifically tailored to highlight the impact of the data distribution in the performance of Q-learning-based algorithms with function approximation, both online and offline. Finally, we experimentally assess the impact of the data distribution properties on the performance of two offline Q-learning-based algorithms under different environments. According to our results: (i) high entropy data distributions are well-suited for learning in an offline manner; and (ii) a certain degree of data diversity (data coverage) and data quality (closeness to optimal policy) are jointly desirable for offline learning.

Autonomous agents that can engage in social interactions witha human is the ultimate goal of a myriad of applications. A keychallenge in the design of these applications is to define the socialbehavior of the agent, which requires extensive content creation.In this research, we explore how we can leverage current state-of-the-art tools to make inferences about the emotional state ofa character in a story as events unfold, in a coherent way. Wepropose a character role-labelling approach to emotion tracking thataccounts for the semantics of emotions. We show that by identifyingactors and objects of events and considering the emotional stateof the characters, we can achieve better performance in this task,when compared to end-to-end approaches.