Matej Jusup

Volodymyr Tkachuk, Seyed Alireza Bakhtiari, Johannes Kirschner et al. · deepmind

A practical challenge in reinforcement learning are combinatorial action spaces that make planning computationally demanding. For example, in cooperative multi-agent reinforcement learning, a potentially large number of agents jointly optimize a global reward function, which leads to a combinatorial blow-up in the action space by the number of agents. As a minimal requirement, we assume access to an argmax oracle that allows to efficiently compute the greedy policy for any Q-function in the model class. Building on recent work in planning with local access to a simulator and linear function approximation, we propose efficient algorithms for this setting that lead to polynomial compute and query complexity in all relevant problem parameters. For the special case where the feature decomposition is additive, we further improve the bounds and extend the results to the kernelized setting with an efficient algorithm.

Matej Jusup, Barna Pásztor, Tadeusz Janik et al.

Many applications, e.g., in shared mobility, require coordinating a large number of agents. Mean-field reinforcement learning addresses the resulting scalability challenge by optimizing the policy of a representative agent interacting with the infinite population of identical agents instead of considering individual pairwise interactions. In this paper, we address an important generalization where there exist global constraints on the distribution of agents (e.g., requiring capacity constraints or minimum coverage requirements to be met). We propose Safe-M$^3$-UCRL, the first model-based mean-field reinforcement learning algorithm that attains safe policies even in the case of unknown transitions. As a key ingredient, it uses epistemic uncertainty in the transition model within a log-barrier approach to ensure pessimistic constraints satisfaction with high probability. Beyond the synthetic swarm motion benchmark, we showcase Safe-M$^3$-UCRL on the vehicle repositioning problem faced by many shared mobility operators and evaluate its performance through simulations built on vehicle trajectory data from a service provider in Shenzhen. Our algorithm effectively meets the demand in critical areas while ensuring service accessibility in regions with low demand.

Petar Steinberg, Juliusz Ziomek, Matej Jusup et al. · oxford

We address the problem of optimising the average payoff for a large number of cooperating agents, where the payoff function is unknown and treated as a black box. While standard Bayesian Optimisation (BO) methods struggle with the scalability required for high-dimensional input spaces, we demonstrate how leveraging the mean-field assumption on the black-box function can transform BO into an efficient and scalable solution. Specifically, we introduce MF-GP-UCB, a novel efficient algorithm designed to optimise agent payoffs in this setting. Our theoretical analysis establishes a regret bound for MF-GP-UCB that is independent of the number of agents, contrasting sharply with the exponential dependence observed when naive BO methods are applied. We evaluate our algorithm on a diverse set of tasks, including real-world problems, such as optimising the location of public bikes for a bike-sharing programme, distributing taxi fleets, and selecting refuelling ports for maritime vessels. Empirical results demonstrate that MF-GP-UCB significantly outperforms existing benchmarks, offering substantial improvements in performance and scalability, constituting a promising solution for mean-field, black-box optimisation. The code is available at https://github.com/petarsteinberg/MF-BO.

John Schultz, Jakub Adamek, Matej Jusup et al. · deepmind

Advancing planning and reasoning capabilities of Large Language Models (LLMs) is one of the key prerequisites towards unlocking their potential for performing reliably in complex and impactful domains. In this paper, we aim to demonstrate this across board games (Chess, Fischer Random / Chess960, Connect Four, and Hex), and we show that search-based planning can yield significant improvements in LLM game-playing strength. We introduce, compare and contrast two major approaches: In external search, the model guides Monte Carlo Tree Search (MCTS) rollouts and evaluations without calls to an external game engine, and in internal search, the model is trained to generate in-context a linearized tree of search and a resulting final choice. Both build on a language model pre-trained on relevant domain knowledge, reliably capturing the transition and value functions in the respective environments, with minimal hallucinations. We evaluate our LLM search implementations against game-specific state-of-the-art engines, showcasing substantial improvements in strength over the base model, and reaching Grandmaster-level performance in chess while operating closer to the human search budget. Our proposed approach, combining search with domain knowledge, is not specific to board games, hinting at more general future applications.

Matej Jusup, Kenan Zhang, Zhiyuan Hu et al.

The rapid expansion of ride-sourcing services such as Uber, Lyft, and Didi Chuxing has fundamentally reshaped urban transportation by offering flexible, on-demand mobility via mobile applications. Despite their convenience, these platforms confront significant operational challenges, particularly vehicle rebalancing - the strategic repositioning of a large group of vehicles to address spatiotemporal mismatches in supply and demand. Inadequate rebalancing not only results in prolonged rider waiting times and inefficient vehicle utilization but also leads to fairness issues, such as the inequitable distribution of service quality and disparities in driver income. To tackle these complexities, we introduce continuous-state mean-field control (MFC) and mean-field reinforcement learning (MFRL) models that employ continuous vehicle repositioning actions. MFC and MFRL offer scalable solutions by modeling each vehicle's behavior through interaction with the vehicle distribution, rather than with individual vehicles. This limits the issues arising from the curse of dimensionality inherent in traditional multi-agent methods, enabling coordination across large fleets with significantly reduced computational complexity. To ensure equitable service access across geographic regions, we integrate an accessibility constraint into both models. Extensive empirical evaluation using real-world data-driven simulation of Shenzhen demonstrates the real-time efficiency and robustness of our approach. Remarkably, it scales to tens of thousands of vehicles, with training times comparable to the decision time of a single linear programming rebalancing. Besides, policies generated by our approach effectively explore the efficiency-equity Pareto front, outperforming conventional benchmarks across key metrics like fleet utilization, fulfilled requests, and pickup distance, while ensuring equitable service access.

Larkin Liu, Shiqi Liu, Yinruo Hua et al.

Markov Decision Processes (MDPs), as a general-purpose framework, often overlook the benefits of incorporating the causal structure of the transition and reward dynamics. For a subclass of resource allocation problems, we introduce the Structurally Decomposed MDP (SD-MDP), which leverages causal disentanglement to partition an MDP's temporal causal graph into independent components. By exploiting this disentanglement, SD-MDP enables dimensionality reduction and computational efficiency gains in optimal value function estimation. We reduce the sequential optimization problem to a fractional knapsack problem with log-linear complexity $O(T \log T)$, outperforming traditional stochastic programming methods that exhibit polynomial complexity with respect to the time horizon $T$. Additionally, SD-MDP's computational advantages are independent of state-action space size, making it viable for high-dimensional spaces. Furthermore, our approach integrates seamlessly with Monte Carlo Tree Search (MCTS), achieving higher expected rewards under constrained simulation budgets while providing a vanishing simple regret bound. Empirical results demonstrate superior policy performance over benchmarks across various logistics and finance domains.