Riccardo Zamboni

Riccardo Zamboni, Mirco Mutti, Marcello Restelli

In reinforcement learning, we typically refer to unsupervised pre-training when we aim to pre-train a policy without a priori access to the task specification, i.e. rewards, to be later employed for efficient learning of downstream tasks. In single-agent settings, the problem has been extensively studied and mostly understood. A popular approach, called task-agnostic exploration, casts the unsupervised objective as maximizing the entropy of the state distribution induced by the agent's policy, from which principles and methods follow. In contrast, little is known about it in multi-agent settings, which are ubiquitous in the real world. What are the pros and cons of alternative problem formulations in this setting? How hard is the problem in theory, how can we solve it in practice? In this paper, we address these questions by first characterizing those alternative formulations and highlighting how the problem, even when tractable in theory, is non-trivial in practice. Then, we present a scalable, decentralized, trust-region policy search algorithm to address the problem in practical settings. Finally, we provide numerical validations to both corroborate the theoretical findings and pave the way for unsupervised multi-agent reinforcement learning via task-agnostic exploration in challenging domains, showing that optimizing for a specific objective, namely mixture entropy, provides an excellent trade-off between tractability and performances.

Vincenzo De Paola, Riccardo Zamboni, Mirco Mutti et al.

Parallel data collection has redefined Reinforcement Learning (RL), unlocking unprecedented efficiency and powering breakthroughs in large-scale real-world applications. In this paradigm, $N$ identical agents operate in $N$ replicas of an environment simulator, accelerating data collection by a factor of $N$. A critical question arises: \textit{Does specializing the policies of the parallel agents hold the key to surpass the $N$ factor acceleration?} In this paper, we introduce a novel learning framework that maximizes the entropy of collected data in a parallel setting. Our approach carefully balances the entropy of individual agents with inter-agent diversity, effectively minimizing redundancies. The latter idea is implemented with a centralized policy gradient method, which shows promise when evaluated empirically against systems of identical agents, as well as synergy with batch RL techniques that can exploit data diversity. Finally, we provide an original concentration analysis that shows faster rates for specialized parallel sampling distributions, which supports our methodology and may be of independent interest.

Riccardo Zamboni, Enrico Brunetti, Marcello Restelli

Offline Reinforcement Learning (RL) focuses on learning policies solely from a batch of previously collected data. offering the potential to leverage such datasets effectively without the need for costly or risky active exploration. While recent advances in Offline Multi-Agent RL (MARL) have shown promise, most existing methods either rely on large datasets jointly collected by all agents or agent-specific datasets collected independently. The former approach ensures strong performance but raises scalability concerns, while the latter emphasizes scalability at the expense of performance guarantees. In this work, we propose a novel scalable routine for both dataset collection and offline learning. Agents first collect diverse datasets coherently with a pre-specified information-sharing network and subsequently learn coherent localized policies without requiring either full observability or falling back to complete decentralization. We theoretically demonstrate that this structured approach allows a multi-agent extension of the seminal Fitted Q-Iteration (FQI) algorithm to globally converge, in high probability, to near-optimal policies. The convergence is subject to error terms that depend on the informativeness of the shared information. Furthermore, we show how this approach allows to bound the inherent error of the supervised-learning phase of FQI with the mutual information between shared and unshared information. Our algorithm, SCAlable Multi-agent FQI (SCAM-FQI), is then evaluated on a distributed decision-making problem. The empirical results align with our theoretical findings, supporting the effectiveness of SCAM-FQI in achieving a balance between scalability and policy performance.

Riccardo Zamboni, Duilio Cirino, Marcello Restelli et al.

The problem of pure exploration in Markov decision processes has been cast as maximizing the entropy over the state distribution induced by the agent's policy, an objective that has been extensively studied. However, little attention has been dedicated to state entropy maximization under partial observability, despite the latter being ubiquitous in applications, e.g., finance and robotics, in which the agent only receives noisy observations of the true state governing the system's dynamics. How can we address state entropy maximization in those domains? In this paper, we study the simple approach of maximizing the entropy over observations in place of true latent states. First, we provide lower and upper bounds to the approximation of the true state entropy that only depends on some properties of the observation function. Then, we show how knowledge of the latter can be exploited to compute a principled regularization of the observation entropy to improve performance. With this work, we provide both a flexible approach to bring advances in state entropy maximization to the POMDP setting and a theoretical characterization of its intrinsic limits.

Riccardo Zamboni, Duilio Cirino, Marcello Restelli et al.

Recent works have studied *state entropy maximization* in reinforcement learning, in which the agent's objective is to learn a policy inducing high entropy over states visitation (Hazan et al., 2019). They typically assume full observability of the state of the system, so that the entropy of the observations is maximized. In practice, the agent may only get *partial* observations, e.g., a robot perceiving the state of a physical space through proximity sensors and cameras. A significant mismatch between the entropy over observations and true states of the system can arise in those settings. In this paper, we address the problem of entropy maximization over the *true states* with a decision policy conditioned on partial observations *only*. The latter is a generalization of POMDPs, which is intractable in general. We develop a memory and computationally efficient *policy gradient* method to address a first-order relaxation of the objective defined on *belief* states, providing various formal characterizations of approximation gaps, the optimization landscape, and the *hallucination* problem. This paper aims to generalize state entropy maximization to more realistic domains that meet the challenges of applications.