We argue that there is a strong connection between ensemble learning and a delegative voting paradigm -- liquid democracy -- that can be leveraged to reduce ensemble training costs. We present an incremental training procedure that identifies and removes redundant classifiers from an ensemble via delegation mechanisms inspired by liquid democracy. Through both analysis and extensive experiments we show that this process greatly reduces the computational cost of training compared to training a full ensemble. By carefully selecting the underlying delegation mechanism, weight centralization in the classifier population is avoided, leading to higher accuracy than some boosting methods. Furthermore, this work serves as an exemplar of how frameworks from computational social choice literature can be applied to problems in nontraditional domains.
We argue that many general evaluation problems can be viewed through the lens of voting theory. Each task is interpreted as a separate voter, which requires only ordinal rankings or pairwise comparisons of agents to produce an overall evaluation. By viewing the aggregator as a social welfare function, we are able to leverage centuries of research in social choice theory to derive principled evaluation frameworks with axiomatic foundations. These evaluations are interpretable and flexible, while avoiding many of the problems currently facing cross-task evaluation. We apply this Voting-as-Evaluation (VasE) framework across multiple settings, including reinforcement learning, large language models, and humans. In practice, we observe that VasE can be more robust than popular evaluation frameworks (Elo and Nash averaging), discovers properties in the evaluation data not evident from scores alone, and can predict outcomes better than Elo in a complex seven-player game. We identify one particular approach, maximal lotteries, that satisfies important consistency properties relevant to evaluation, is computationally efficient (polynomial in the size of the evaluation data), and identifies game-theoretic cycles.
While it has long been recognized that a team of individual learning agents can be greater than the sum of its parts, recent work has shown that larger teams are not necessarily more effective than smaller ones. In this paper, we study why and under which conditions certain team structures promote effective learning for a population of individual learning agents. We show that, depending on the environment, some team structures help agents learn to specialize into specific roles, resulting in more favorable global results. However, large teams create credit assignment challenges that reduce coordination, leading to large teams performing poorly compared to smaller ones. We support our conclusions with both theoretical analysis and empirical results.
A central design problem in game theoretic analysis is the estimation of the players' utilities. In many real-world interactive situations of human decision making, including human driving, the utilities are multi-objective in nature; therefore, estimating the parameters of aggregation, i.e., mapping of multi-objective utilities to a scalar value, becomes an essential part of game construction. However, estimating this parameter from observational data introduces several challenges due to a host of unobservable factors, including the underlying modality of aggregation and the possibly boundedly rational behaviour model that generated the observation. Based on the concept of rationalisability, we develop algorithms for estimating multi-objective aggregation parameters for two common aggregation methods, weighted and satisficing aggregation, and for both strategic and non-strategic reasoning models. Based on three different datasets, we provide insights into how human drivers aggregate the utilities of safety and progress, as well as the situational dependence of the aggregation process. Additionally, we show that irrespective of the specific solution concept used for solving the games, a data-driven estimation of utility aggregation significantly improves the predictive accuracy of behaviour models with respect to observed human behaviour.
Multiagent reinforcement learning (MARL) has benefited significantly from population-based and game-theoretic training regimes. One approach, Policy-Space Response Oracles (PSRO), employs standard reinforcement learning to compute response policies via approximate best responses and combines them via meta-strategy selection. We augment PSRO by adding a novel search procedure with generative sampling of world states, and introduce two new meta-strategy solvers based on the Nash bargaining solution. We evaluate PSRO's ability to compute approximate Nash equilibrium, and its performance in two negotiation games: Colored Trails, and Deal or No Deal. We conduct behavioral studies where human participants negotiate with our agents ($N = 346$). We find that search with generative modeling finds stronger policies during both training time and test time, enables online Bayesian co-player prediction, and can produce agents that achieve comparable social welfare negotiating with humans as humans trading among themselves.
Multi-agent reinforcement learning typically suffers from the problem of sample inefficiency, where learning suitable policies involves the use of many data samples. Learning from external demonstrators is a possible solution that mitigates this problem. However, most prior approaches in this area assume the presence of a single demonstrator. Leveraging multiple knowledge sources (i.e., advisors) with expertise in distinct aspects of the environment could substantially speed up learning in complex environments. This paper considers the problem of simultaneously learning from multiple independent advisors in multi-agent reinforcement learning. The approach leverages a two-level Q-learning architecture, and extends this framework from single-agent to multi-agent settings. We provide principled algorithms that incorporate a set of advisors by both evaluating the advisors at each state and subsequently using the advisors to guide action selection. We also provide theoretical convergence and sample complexity guarantees. Experimentally, we validate our approach in three different test-beds and show that our algorithms give better performances than baselines, can effectively integrate the combined expertise of different advisors, and learn to ignore bad advice.
The Game Theory & Multi-Agent team at DeepMind studies several aspects of multi-agent learning ranging from computing approximations to fundamental concepts in game theory to simulating social dilemmas in rich spatial environments and training 3-d humanoids in difficult team coordination tasks. A signature aim of our group is to use the resources and expertise made available to us at DeepMind in deep reinforcement learning to explore multi-agent systems in complex environments and use these benchmarks to advance our understanding. Here, we summarise the recent work of our team and present a taxonomy that we feel highlights many important open challenges in multi-agent research.
For problems requiring cooperation, many multiagent systems implement solutions among either individual agents or across an entire population towards a common goal. Multiagent teams are primarily studied when in conflict; however, organizational psychology (OP) highlights the benefits of teams among human populations for learning how to coordinate and cooperate. In this paper, we propose a new model of multiagent teams for reinforcement learning (RL) agents inspired by OP and early work on teams in artificial intelligence. We validate our model using complex social dilemmas that are popular in recent multiagent RL and find that agents divided into teams develop cooperative pro-social policies despite incentives to not cooperate. Furthermore, agents are better able to coordinate and learn emergent roles within their teams and achieve higher rewards compared to when the interests of all agents are aligned.
We propose a model for multi-objective optimization, a credo, for agents in a system that are configured into multiple groups (i.e., teams). Our model of credo regulates how agents optimize their behavior for the component groups they belong to. We evaluate credo in the context of challenging social dilemmas with reinforcement learning agents. Our results indicate that the interests of teammates, or the entire system, are not required to be fully aligned for globally beneficial outcomes. We identify two scenarios without full common interest that achieve high equality and significantly higher mean population rewards compared to when the interests of all agents are aligned.
In the last decade, there have been significant advances in multi-agent reinforcement learning (MARL) but there are still numerous challenges, such as high sample complexity and slow convergence to stable policies, that need to be overcome before wide-spread deployment is possible. However, many real-world environments already, in practice, deploy sub-optimal or heuristic approaches for generating policies. An interesting question which arises is how to best use such approaches as advisors to help improve reinforcement learning in multi-agent domains. In this paper, we provide a principled framework for incorporating action recommendations from online sub-optimal advisors in multi-agent settings. We describe the problem of ADvising Multiple Intelligent Reinforcement Agents (ADMIRAL) in nonrestrictive general-sum stochastic game environments and present two novel Q-learning based algorithms: ADMIRAL - Decision Making (ADMIRAL-DM) and ADMIRAL - Advisor Evaluation (ADMIRAL-AE), which allow us to improve learning by appropriately incorporating advice from an advisor (ADMIRAL-DM), and evaluate the effectiveness of an advisor (ADMIRAL-AE). We analyze the algorithms theoretically and provide fixed-point guarantees regarding their learning in general-sum stochastic games. Furthermore, extensive experiments illustrate that these algorithms: can be used in a variety of environments, have performances that compare favourably to other related baselines, can scale to large state-action spaces, and are robust to poor advice from advisors.