Jacopo Castellini

Johan Peralez, Aurèlien Delage, Jacopo Castellini et al.

The centralized training for decentralized execution paradigm emerged as the state-of-the-art approach to $ε$-optimally solving decentralized partially observable Markov decision processes. However, scalability remains a significant issue. This paper presents a novel and more scalable alternative, namely the sequential-move centralized training for decentralized execution. This paradigm further pushes the applicability of the Bellman's principle of optimality, raising three new properties. First, it allows a central planner to reason upon sufficient sequential-move statistics instead of prior simultaneous-move ones. Next, it proves that $ε$-optimal value functions are piecewise linear and convex in such sufficient sequential-move statistics. Finally, it drops the complexity of the backup operators from double exponential to polynomial at the expense of longer planning horizons. Besides, it makes it easy to use single-agent methods, e.g., SARSA algorithm enhanced with these findings, while still preserving convergence guarantees. Experiments on two- as well as many-agent domains from the literature against $ε$-optimal simultaneous-move solvers confirm the superiority of our novel approach. This paradigm opens the door for efficient planning and reinforcement learning methods for multi-agent systems.

Rafael F. Cunha, Jacopo Castellini, Johan Peralez et al.

Multi-agent planning and reinforcement learning can be challenging when agents cannot see the state of the world or communicate with each other due to communication costs, latency, or noise. Partially Observable Stochastic Games (POSGs) provide a mathematical framework for modelling such scenarios. This paper aims to improve the efficiency of planning and reinforcement learning algorithms for POSGs by identifying the underlying structure of optimal state-value functions. The approach involves reformulating the original game from the perspective of a trusted third party who plans on behalf of the agents simultaneously. From this viewpoint, the original POSGs can be viewed as Markov games where states are occupancy states, \ie posterior probability distributions over the hidden states of the world and the stream of actions and observations that agents have experienced so far. This study mainly proves that the optimal state-value function is a convex function of occupancy states expressed on an appropriate basis in all zero-sum, common-payoff, and Stackelberg POSGs.

Jacopo Castellini, Sam Devlin, Frans A. Oliehoek et al.

Policy gradient methods have become one of the most popular classes of algorithms for multi-agent reinforcement learning. A key challenge, however, that is not addressed by many of these methods is multi-agent credit assignment: assessing an agent's contribution to the overall performance, which is crucial for learning good policies. We propose a novel algorithm called Dr.Reinforce that explicitly tackles this by combining difference rewards with policy gradients to allow for learning decentralized policies when the reward function is known. By differencing the reward function directly, Dr.Reinforce avoids difficulties associated with learning the Q-function as done by Counterfactual Multiagent Policy Gradients (COMA), a state-of-the-art difference rewards method. For applications where the reward function is unknown, we show the effectiveness of a version of Dr.Reinforce that learns an additional reward network that is used to estimate the difference rewards.

Jacopo Castellini

One of the main problems encountered so far with recurrent neural networks is that they struggle to retain long-time information dependencies in their recurrent connections. Neural Turing Machines (NTMs) attempt to mitigate this issue by providing the neural network with an external portion of memory, in which information can be stored and manipulated later on. The whole mechanism is differentiable end-to-end, allowing the network to learn how to utilise this long-term memory via stochastic gradient descent. This allows NTMs to infer simple algorithms directly from data sequences. Nonetheless, the model can be hard to train due to a large number of parameters and interacting components and little related work is present. In this work we use NTMs to learn and generalise two arithmetical tasks: binary addition and multiplication. These tasks are two fundamental algorithmic examples in computer science, and are a lot more challenging than the previously explored ones, with which we aim to shed some light on the real capabilities on this neural model.