Frans A. Oliehoek

Aleksander Czechowski, Frans A. Oliehoek

One of the main challenges of multi-agent learning lies in establishing convergence of the algorithms, as, in general, a collection of individual, self-serving agents is not guaranteed to converge with their joint policy, when learning concurrently. This is in stark contrast to most single-agent environments, and sets a prohibitive barrier for deployment in practical applications, as it induces uncertainty in long term behavior of the system. In this work, we apply the concept of trapping regions, known from qualitative theory of dynamical systems, to create safety sets in the joint strategy space for decentralized learning. We propose a binary partitioning algorithm for verification that candidate sets form trapping regions in systems with known learning dynamics, and a heuristic sampling algorithm for scenarios where learning dynamics are not known. We demonstrate the applications to a regularized version of Dirac Generative Adversarial Network, a four-intersection traffic control scenario run in a state of the art open-source microscopic traffic simulator SUMO, and a mathematical model of economic competition.

Mustafa Mert Çelikok, Frans A. Oliehoek, Samuel Kaski

Centaurs are half-human, half-AI decision-makers where the AI's goal is to complement the human. To do so, the AI must be able to recognize the goals and constraints of the human and have the means to help them. We present a novel formulation of the interaction between the human and the AI as a sequential game where the agents are modelled using Bayesian best-response models. We show that in this case the AI's problem of helping bounded-rational humans make better decisions reduces to a Bayes-adaptive POMDP. In our simulated experiments, we consider an instantiation of our framework for humans who are subjectively optimistic about the AI's future behaviour. Our results show that when equipped with a model of the human, the AI can infer the human's bounds and nudge them towards better decisions. We discuss ways in which the machine can learn to improve upon its own limitations as well with the help of the human. We identify a novel trade-off for centaurs in partially observable tasks: for the AI's actions to be acceptable to the human, the machine must make sure their beliefs are sufficiently aligned, but aligning beliefs might be costly. We present a preliminary theoretical analysis of this trade-off and its dependence on task structure.

Miguel Suau, Matthijs T. J. Spaan, Frans A. Oliehoek

Reinforcement learning agents tend to develop habits that are effective only under specific policies. Following an initial exploration phase where agents try out different actions, they eventually converge onto a particular policy. As this occurs, the distribution over state-action trajectories becomes narrower, leading agents to repeatedly experience the same transitions. This repetitive exposure fosters spurious correlations between certain observations and rewards. Agents may then pick up on these correlations and develop simplistic habits tailored to the specific set of trajectories dictated by their policy. The problem is that these habits may yield incorrect outcomes when agents are forced to deviate from their typical trajectories, prompted by changes in the environment. This paper presents a mathematical characterization of this phenomenon, termed policy confounding, and illustrates, through a series of examples, the circumstances under which it occurs.

Zuzanna Osika, Jazmin Zatarain Salazar, Diederik M. Roijers et al.

We present a review that unifies decision-support methods for exploring the solutions produced by multi-objective optimization (MOO) algorithms. As MOO is applied to solve diverse problems, approaches for analyzing the trade-offs offered by MOO algorithms are scattered across fields. We provide an overview of the advances on this topic, including methods for visualization, mining the solution set, and uncertainty exploration as well as emerging research directions, including interactivity, explainability, and ethics. We synthesize these methods drawing from different fields of research to build a unified approach, independent of the application. Our goals are to reduce the entry barrier for researchers and practitioners on using MOO algorithms and to provide novel research directions.

Jinke He, Thomas M. Moerland, Joery A. de Vries et al.

Model-based reinforcement learning (MBRL) has drawn considerable interest in recent years, given its promise to improve sample efficiency. Moreover, when using deep-learned models, it is possible to learn compact and generalizable models from data. In this work, we study MuZero, a state-of-the-art deep model-based reinforcement learning algorithm that distinguishes itself from existing algorithms by learning a value-equivalent model. Despite MuZero's success and impact in the field of MBRL, existing literature has not thoroughly addressed why MuZero performs so well in practice. Specifically, there is a lack of in-depth investigation into the value-equivalent model learned by MuZero and its effectiveness in model-based credit assignment and policy improvement, which is vital for achieving sample efficiency in MBRL. To fill this gap, we explore two fundamental questions through our empirical analysis: 1) to what extent does MuZero achieve its learning objective of a value-equivalent model, and 2) how useful are these models for policy improvement? Our findings reveal that MuZero's model struggles to generalize when evaluating unseen policies, which limits its capacity for additional policy improvement. However, MuZero's incorporation of the policy prior in MCTS alleviates this problem, which biases the search towards actions where the model is more accurate.

Rolf A. N. Starre, Marco Loog, Elena Congeduti et al.

Many methods for Model-based Reinforcement learning (MBRL) in Markov decision processes (MDPs) provide guarantees for both the accuracy of the model they can deliver and the learning efficiency. At the same time, state abstraction techniques allow for a reduction of the size of an MDP while maintaining a bounded loss with respect to the original problem. Therefore, it may come as a surprise that no such guarantees are available when combining both techniques, i.e., where MBRL merely observes abstract states. Our theoretical analysis shows that abstraction can introduce a dependence between samples collected online (e.g., in the real world). That means that, without taking this dependence into account, results for MBRL do not directly extend to this setting. Our result shows that we can use concentration inequalities for martingales to overcome this problem. This result makes it possible to extend the guarantees of existing MBRL algorithms to the setting with abstraction. We illustrate this by combining R-MAX, a prototypical MBRL algorithm, with abstraction, thus producing the first performance guarantees for model-based 'RL from Abstracted Observations': model-based reinforcement learning with an abstract model.

Robert Loftin, Frans A. Oliehoek

Learning to cooperate with other agents is challenging when those agents also possess the ability to adapt to our own behavior. Practical and theoretical approaches to learning in cooperative settings typically assume that other agents' behaviors are stationary, or else make very specific assumptions about other agents' learning processes. The goal of this work is to understand whether we can reliably learn to cooperate with other agents without such restrictive assumptions, which are unlikely to hold in real-world applications. Our main contribution is a set of impossibility results, which show that no learning algorithm can reliably learn to cooperate with all possible adaptive partners in a repeated matrix game, even if that partner is guaranteed to cooperate with some stationary strategy. Motivated by these results, we then discuss potential alternative assumptions which capture the idea that an adaptive partner will only adapt rationally to our behavior.

Miguel Suau, Jinke He, Mustafa Mert Çelikok et al.

Due to its high sample complexity, simulation is, as of today, critical for the successful application of reinforcement learning. Many real-world problems, however, exhibit overly complex dynamics, which makes their full-scale simulation computationally slow. In this paper, we show how to decompose large networked systems of many agents into multiple local components such that we can build separate simulators that run independently and in parallel. To monitor the influence that the different local components exert on one another, each of these simulators is equipped with a learned model that is periodically trained on real trajectories. Our empirical results reveal that distributing the simulation among different processes not only makes it possible to train large multi-agent systems in just a few hours but also helps mitigate the negative effects of simultaneous learning.

Raphael Avalos, Eugenio Bargiacchi, Ann Nowé et al.

In key real-world problems, full state information is sometimes available but only at a high cost, like activating precise yet energy-intensive sensors or consulting humans, thereby compelling the agent to operate under partial observability. For this scenario, we propose AEMS-SR (Anytime Error Minimization Search with State Requests), a principled online planning algorithm tailored for POMDPs with state requests. By representing the search space as a graph instead of a tree, AEMS-SR avoids the exponential growth of the search space originating from state requests. Theoretical analysis demonstrates AEMS-SR's $\varepsilon$-optimality, ensuring solution quality, while empirical evaluations illustrate its effectiveness compared with AEMS and POMCP, two SOTA online planning algorithms. AEMS-SR enables efficient planning in domains characterized by partial observability and costly state requests offering practical benefits across various applications.

Robert Loftin, Mustafa Mert Çelikok, Herke van Hoof et al.

In multi-agent problems requiring a high degree of cooperation, success often depends on the ability of the agents to adapt to each other's behavior. A natural solution concept in such settings is the Stackelberg equilibrium, in which the ``leader'' agent selects the strategy that maximizes its own payoff given that the ``follower'' agent will choose their best response to this strategy. Recent work has extended this solution concept to two-player differentiable games, such as those arising from multi-agent deep reinforcement learning, in the form of the \textit{differential} Stackelberg equilibrium. While this previous work has presented learning dynamics which converge to such equilibria, these dynamics are ``coupled'' in the sense that the learning updates for the leader's strategy require some information about the follower's payoff function. As such, these methods cannot be applied to truly decentralised multi-agent settings, particularly ad hoc cooperation, where each agent only has access to its own payoff function. In this work we present ``uncoupled'' learning dynamics based on zeroth-order gradient estimators, in which each agent's strategy update depends only on their observations of the other's behavior. We analyze the convergence of these dynamics in general-sum games, and prove that they converge to differential Stackelberg equilibria under the same conditions as previous coupled methods. Furthermore, we present an online mechanism by which symmetric learners can negotiate leader-follower roles. We conclude with a discussion of the implications of our work for multi-agent reinforcement learning and ad hoc collaboration more generally.

Ariyan Bighashdel, Thiago D. Simão, Frans A. Oliehoek

Multi-agent reinforcement learning (MARL) offers a scalable alternative to exact game-theoretic analysis but suffers from non-stationarity and the need to maintain diverse populations of strategies that capture non-transitive interactions. Policy Space Response Oracles (PSRO) address these issues by iteratively expanding a restricted game with approximate best responses (BRs), yet per-agent BR training makes it prohibitively expensive in many-agent or simulator-expensive settings. We introduce Joint Experience Best Response (JBR), a drop-in modification to PSRO that collects trajectories once under the current meta-strategy profile and reuses this joint dataset to compute BRs for all agents simultaneously. This amortizes environment interaction and improves the sample efficiency of best-response computation. Because JBR converts BR computation into an offline RL problem, we propose three remedies for distribution-shift bias: (i) Conservative JBR with safe policy improvement, (ii) Exploration-Augmented JBR that perturbs data collection and admits theoretical guarantees, and (iii) Hybrid BR that interleaves JBR with periodic independent BR updates. Across benchmark multi-agent environments, Exploration-Augmented JBR achieves the best accuracy-efficiency trade-off, while Hybrid BR attains near-PSRO performance at a fraction of the sample cost. Overall, JBR makes PSRO substantially more practical for large-scale strategic learning while preserving equilibrium robustness.

Daniel De Dios Allegue, Jinke He, Frans A. Oliehoek

Transformers have shown strong ability to model long-term dependencies and are increasingly adopted as world models in model-based reinforcement learning (RL) under partial observability. However, unlike natural language corpora, RL trajectories are sparse and reward-driven, making standard self-attention inefficient because it distributes weight uniformly across all past tokens rather than emphasizing the few transitions critical for control. To address this, we introduce structured inductive priors into the self-attention mechanism of the dynamics head: (i) per-head memory-length priors that constrain attention to task-specific windows, and (ii) distributional priors that learn smooth Gaussian weightings over past state-action pairs. We integrate these mechanisms into UniZero, a model-based RL agent with a Transformer-based world model that supports planning under partial observability. Experiments on the Atari 100k benchmark show that most efficiency gains arise from the Gaussian prior, which smoothly allocates attention to informative transitions, while memory-length priors often truncate useful signals with overly restrictive cut-offs. In particular, Gaussian Attention achieves a 77% relative improvement in mean human-normalized scores over UniZero. These findings suggest that in partially observable RL domains with non-stationary temporal dependencies, discrete memory windows are difficult to learn reliably, whereas smooth distributional priors flexibly adapt across horizons and yield more robust data efficiency. Overall, our results demonstrate that encoding structured temporal priors directly into self-attention improves the prioritization of informative histories for dynamics modeling under partial observability.

Ariyan Bighashdel, Yongzhao Wang, Stephen McAleer et al.

Game theory provides a mathematical way to study the interaction between multiple decision makers. However, classical game-theoretic analysis is limited in scalability due to the large number of strategies, precluding direct application to more complex scenarios. This survey provides a comprehensive overview of a framework for large games, known as Policy Space Response Oracles (PSRO), which holds promise to improve scalability by focusing attention on sufficient subsets of strategies. We first motivate PSRO and provide historical context. We then focus on the strategy exploration problem for PSRO: the challenge of assembling effective subsets of strategies that still represent the original game well with minimum computational cost. We survey current research directions for enhancing the efficiency of PSRO, and explore the applications of PSRO across various domains. We conclude by discussing open questions and future research.

Zuzanna Osika, Jazmin Zatarain-Salazar, Frans A. Oliehoek et al.

Multi-objective reinforcement learning (MORL) is used to solve problems involving multiple objectives. An MORL agent must make decisions based on the diverse signals provided by distinct reward functions. Training an MORL agent yields a set of solutions (policies), each presenting distinct trade-offs among the objectives (expected returns). MORL enhances explainability by enabling fine-grained comparisons of policies in the solution set based on their trade-offs as opposed to having a single policy. However, the solution set is typically large and multi-dimensional, where each policy (e.g., a neural network) is represented by its objective values. We propose an approach for clustering the solution set generated by MORL. By considering both policy behavior and objective values, our clustering method can reveal the relationship between policy behaviors and regions in the objective space. This approach can enable decision makers (DMs) to identify overarching trends and insights in the solution set rather than examining each policy individually. We tested our method in four multi-objective environments and found it outperformed traditional k-medoids clustering. Additionally, we include a case study that demonstrates its real-world application.

Davide Mambelli, Stephan Bongers, Onno Zoeter et al.

Policy gradient methods are widely adopted reinforcement learning algorithms for tasks with continuous action spaces. These methods succeeded in many application domains, however, because of their notorious sample inefficiency their use remains limited to problems where fast and accurate simulations are available. A common way to improve sample efficiency is to modify their objective function to be computable from off-policy samples without importance sampling. A well-established off-policy objective is the excursion objective. This work studies the difference between the excursion objective and the traditional on-policy objective, which we refer to as the on-off gap. We provide the first theoretical analysis showing conditions to reduce the on-off gap while establishing empirical evidence of shortfalls arising when these conditions are not met.

Wook Lee, Frans A. Oliehoek

Leveraging machine learning methods to solve constraint satisfaction problems has shown promising, but they are mostly limited to a static situation where the problem description is completely known and fixed from the beginning. In this work we present a new approach to constraint satisfaction and optimization in dynamically changing environments, particularly when variables in the problem are statistically independent. We frame it as a reinforcement learning problem and introduce a conditional policy generator by borrowing the idea of class conditional generative adversarial networks (GANs). Assuming that the problem includes both static and dynamic constraints, the former are used in a reward formulation to guide the policy training such that it learns to map to a probabilistic distribution of solutions satisfying static constraints from a noise prior, which is similar to a generator in GANs. On the other hand, dynamic constraints in the problem are encoded to different class labels and fed with the input noise. The policy is then simultaneously updated for maximum likelihood of correctly classifying given the dynamic conditions in a supervised manner. We empirically demonstrate a proof-of-principle experiment with a multi-modal constraint satisfaction problem and compare between unconditional and conditional cases.

Palok Biswas, Zuzanna Osika, Isidoro Tamassia et al.

Addressing climate change requires coordinated policy efforts of nations worldwide. These efforts are informed by scientific reports, which rely in part on Integrated Assessment Models (IAMs), prominent tools used to assess the economic impacts of climate policies. However, traditional IAMs optimize policies based on a single objective, limiting their ability to capture the trade-offs among economic growth, temperature goals, and climate justice. As a result, policy recommendations have been criticized for perpetuating inequalities, fueling disagreements during policy negotiations. We introduce Justice, the first framework integrating IAM with Multi-Objective Multi-Agent Reinforcement Learning (MOMARL). By incorporating multiple objectives, Justice generates policy recommendations that shed light on equity while balancing climate and economic goals. Further, using multiple agents can provide a realistic representation of the interactions among the diverse policy actors. We identify equitable Pareto-optimal policies using our framework, which facilitates deliberative decision-making by presenting policymakers with the inherent trade-offs in climate and economic policy.

Yiman Bao, Jie Gao, Jinke He et al.

Efficient timing in ride-matching is crucial for improving the performance of ride-hailing and ride-pooling services, as it determines the number of drivers and passengers considered in each matching process. Traditional batched matching methods often use fixed time intervals to accumulate ride requests before assigning matches. While this approach increases the number of available drivers and passengers for matching, it fails to adapt to real-time supply-demand fluctuations, often leading to longer passenger wait times and driver idle periods. To address this limitation, we propose an adaptive ride-matching strategy using deep reinforcement learning (RL) to dynamically determine when to perform matches based on real-time system conditions. Unlike fixed-interval approaches, our method continuously evaluates system states and executes matching at moments that minimize total passenger wait time. Additionally, we incorporate a potential-based reward shaping (PBRS) mechanism to mitigate sparse rewards, accelerating RL training and improving decision quality. Extensive empirical evaluations using a realistic simulator trained on real-world data demonstrate that our approach outperforms fixed-interval matching strategies, significantly reducing passenger waiting times and detour delays, thereby enhancing the overall efficiency of ride-hailing and ride-pooling systems.

Hüseyin Aydın, Kevin Godin-Dubois, Libio Goncalvez Braz et al.

Reinforcement learning (RL) offers a general approach for modeling and training AI agents, including human-AI interaction scenarios. In this paper, we propose SHARPIE (Shared Human-AI Reinforcement Learning Platform for Interactive Experiments) to address the need for a generic framework to support experiments with RL agents and humans. Its modular design consists of a versatile wrapper for RL environments and algorithm libraries, a participant-facing web interface, logging utilities, deployment on popular cloud and participant recruitment platforms. It empowers researchers to study a wide variety of research questions related to the interaction between humans and RL agents, including those related to interactive reward specification and learning, learning from human feedback, action delegation, preference elicitation, user-modeling, and human-AI teaming. The platform is based on a generic interface for human-RL interactions that aims to standardize the field of study on RL in human contexts.

Catalin E. Brita, Stephan Bongers, Frans A. Oliehoek

In offline reinforcement learning, deriving an effective policy from a pre-collected set of experiences is challenging due to the distribution mismatch between the target policy and the behavioral policy used to collect the data, as well as the limited sample size. Model-based reinforcement learning improves sample efficiency by generating simulated experiences using a learned dynamic model of the environment. However, these synthetic experiences often suffer from the same distribution mismatch. To address these challenges, we introduce SimuDICE, a framework that iteratively refines the initial policy derived from offline data using synthetically generated experiences from the world model. SimuDICE enhances the quality of these simulated experiences by adjusting the sampling probabilities of state-action pairs based on stationary DIstribution Correction Estimation (DICE) and the estimated confidence in the model's predictions. This approach guides policy improvement by balancing experiences similar to those frequently encountered with ones that have a distribution mismatch. Our experiments show that SimuDICE achieves performance comparable to existing algorithms while requiring fewer pre-collected experiences and planning steps, and it remains robust across varying data collection policies.

Robert Loftin, Mustafa Mert Çelikok, Frans A. Oliehoek

Multiagent systems deployed in the real world need to cooperate with other agents (including humans) nearly as effectively as these agents cooperate with one another. To design such AI, and provide guarantees of its effectiveness, we need to clearly specify what types of agents our AI must be able to cooperate with. In this work we propose a generic model of socially intelligent agents, which are individually rational learners that are also able to cooperate with one another (in the sense that their joint behavior is Pareto efficient). We define rationality in terms of the regret incurred by each agent over its lifetime, and show how we can construct socially intelligent agents for different forms of regret. We then discuss the implications of this model for the development of "robust" MAS that can cooperate with a wide variety of socially intelligent agents.

Sammie Katt, Hai Nguyen, Frans A. Oliehoek et al.

While reinforcement learning (RL) has made great advances in scalability, exploration and partial observability are still active research topics. In contrast, Bayesian RL (BRL) provides a principled answer to both state estimation and the exploration-exploitation trade-off, but struggles to scale. To tackle this challenge, BRL frameworks with various prior assumptions have been proposed, with varied success. This work presents a representation-agnostic formulation of BRL under partially observability, unifying the previous models under one theoretical umbrella. To demonstrate its practical significance we also propose a novel derivation, Bayes-Adaptive Deep Dropout rl (BADDr), based on dropout networks. Under this parameterization, in contrast to previous work, the belief over the state and dynamics is a more scalable inference problem. We choose actions through Monte-Carlo tree search and empirically show that our method is competitive with state-of-the-art BRL methods on small domains while being able to solve much larger ones.

Miguel Suau, Jinke He, Matthijs T. J. Spaan et al.

Learning effective policies for real-world problems is still an open challenge for the field of reinforcement learning (RL). The main limitation being the amount of data needed and the pace at which that data can be obtained. In this paper, we study how to build lightweight simulators of complicated systems that can run sufficiently fast for deep RL to be applicable. We focus on domains where agents interact with a reduced portion of a larger environment while still being affected by the global dynamics. Our method combines the use of local simulators with learned models that mimic the influence of the global system. The experiments reveal that incorporating this idea into the deep RL workflow can considerably accelerate the training process and presents several opportunities for the future.

Jinke He, Miguel Suau, Hendrik Baier et al.

How can we plan efficiently in a large and complex environment when the time budget is limited? Given the original simulator of the environment, which may be computationally very demanding, we propose to learn online an approximate but much faster simulator that improves over time. To plan reliably and efficiently while the approximate simulator is learning, we develop a method that adaptively decides which simulator to use for every simulation, based on a statistic that measures the accuracy of the approximate simulator. This allows us to use the approximate simulator to replace the original simulator for faster simulations when it is accurate enough under the current context, thus trading off simulation speed and accuracy. Experimental results in two large domains show that when integrated with POMCP, our approach allows to plan with improving efficiency over time.

Markus Peschl, Arkady Zgonnikov, Frans A. Oliehoek et al.

Inferring reward functions from demonstrations and pairwise preferences are auspicious approaches for aligning Reinforcement Learning (RL) agents with human intentions. However, state-of-the art methods typically focus on learning a single reward model, thus rendering it difficult to trade off different reward functions from multiple experts. We propose Multi-Objective Reinforced Active Learning (MORAL), a novel method for combining diverse demonstrations of social norms into a Pareto-optimal policy. Through maintaining a distribution over scalarization weights, our approach is able to interactively tune a deep RL agent towards a variety of preferences, while eliminating the need for computing multiple policies. We empirically demonstrate the effectiveness of MORAL in two scenarios, which model a delivery and an emergency task that require an agent to act in the presence of normative conflicts. Overall, we consider our research a step towards multi-objective RL with learned rewards, bridging the gap between current reward learning and machine ethics literature.

Elise van der Pol, Herke van Hoof, Frans A. Oliehoek et al.

This paper introduces Multi-Agent MDP Homomorphic Networks, a class of networks that allows distributed execution using only local information, yet is able to share experience between global symmetries in the joint state-action space of cooperative multi-agent systems. In cooperative multi-agent systems, complex symmetries arise between different configurations of the agents and their local observations. For example, consider a group of agents navigating: rotating the state globally results in a permutation of the optimal joint policy. Existing work on symmetries in single agent reinforcement learning can only be generalized to the fully centralized setting, because such approaches rely on the global symmetry in the full state-action spaces, and these can result in correspondences across agents. To encode such symmetries while still allowing distributed execution we propose a factorization that decomposes global symmetries into local transformations. Our proposed factorization allows for distributing the computation that enforces global symmetries over local agents and local interactions. We introduce a multi-agent equivariant policy network based on this factorization. We show empirically on symmetric multi-agent problems that globally symmetric distributable policies improve data efficiency compared to non-equivariant baselines.

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.

Wook Lee, Frans A. Oliehoek

In this work, we present a learning based approach to analog circuit design, where the goal is to optimize circuit performance subject to certain design constraints. One of the aspects that makes this problem challenging to optimize, is that measuring the performance of candidate configurations with simulation can be computationally expensive, particularly in the post-layout design. Additionally, the large number of design constraints and the interaction between the relevant quantities makes the problem complex. Therefore, to better facilitate supporting the human designers, it is desirable to gain knowledge about the whole space of feasible solutions. In order to tackle these challenges, we take inspiration from model-based reinforcement learning and propose a method with two key properties. First, it learns a reward model, i.e., surrogate model of the performance approximated by neural networks, to reduce the required number of simulation. Second, it uses a stochastic policy generator to explore the diverse solution space satisfying constraints. Together we combine these in a Dyna-style optimization framework, which we call DynaOpt, and empirically evaluate the performance on a circuit benchmark of a two-stage operational amplifier. The results show that, compared to the model-free method applied with 20,000 circuit simulations to train the policy, DynaOpt achieves even much better performance by learning from scratch with only 500 simulations.

Elena Congeduti, Alexander Mey, Frans A. Oliehoek

Sequential decision making techniques hold great promise to improve the performance of many real-world systems, but computational complexity hampers their principled application. Influence-based abstraction aims to gain leverage by modeling local subproblems together with the 'influence' that the rest of the system exerts on them. While computing exact representations of such influence might be intractable, learning approximate representations offers a promising approach to enable scalable solutions. This paper investigates the performance of such approaches from a theoretical perspective. The primary contribution is the derivation of sufficient conditions on approximate influence representations that can guarantee solutions with small value loss. In particular we show that neural networks trained with cross entropy are well suited to learn approximate influence representations. Moreover, we provide a sample based formulation of the bounds, which reduces the gap to applications. Finally, driven by our theoretical insights, we propose approximation error estimators, which empirically reveal to correlate well with the value loss.

Mikko Lauri, Frans A. Oliehoek

Multi-agent active perception is a task where a team of agents cooperatively gathers observations to compute a joint estimate of a hidden variable. The task is decentralized and the joint estimate can only be computed after the task ends by fusing observations of all agents. The objective is to maximize the accuracy of the estimate. The accuracy is quantified by a centralized prediction reward determined by a centralized decision-maker who perceives the observations gathered by all agents after the task ends. In this paper, we model multi-agent active perception as a decentralized partially observable Markov decision process (Dec-POMDP) with a convex centralized prediction reward. We prove that by introducing individual prediction actions for each agent, the problem is converted into a standard Dec-POMDP with a decentralized prediction reward. The loss due to decentralization is bounded, and we give a sufficient condition for when it is zero. Our results allow application of any Dec-POMDP solution algorithm to multi-agent active perception problems, and enable planning to reduce uncertainty without explicit computation of joint estimates. We demonstrate the empirical usefulness of our results by applying a standard Dec-POMDP algorithm to multi-agent active perception problems, showing increased scalability in the planning horizon.

Jinke He, Miguel Suau, Frans A. Oliehoek

How can we plan efficiently in real time to control an agent in a complex environment that may involve many other agents? While existing sample-based planners have enjoyed empirical success in large POMDPs, their performance heavily relies on a fast simulator. However, real-world scenarios are complex in nature and their simulators are often computationally demanding, which severely limits the performance of online planners. In this work, we propose influence-augmented online planning, a principled method to transform a factored simulator of the entire environment into a local simulator that samples only the state variables that are most relevant to the observation and reward of the planning agent and captures the incoming influence from the rest of the environment using machine learning methods. Our main experimental results show that planning on this less accurate but much faster local simulator with POMCP leads to higher real-time planning performance than planning on the simulator that models the entire environment.

Yash Satsangi, Shimon Whiteson, Frans A. Oliehoek et al.

In active perception tasks, an agent aims to select sensory actions that reduce its uncertainty about one or more hidden variables. While partially observable Markov decision processes (POMDPs) provide a natural model for such problems, reward functions that directly penalize uncertainty in the agent's belief can remove the piecewise-linear and convex property of the value function required by most POMDP planners. Furthermore, as the number of sensors available to the agent grows, the computational cost of POMDP planning grows exponentially with it, making POMDP planning infeasible with traditional methods. In this article, we address a twofold challenge of modeling and planning for active perception tasks. We show the mathematical equivalence of $ρ$POMDP and POMDP-IR, two frameworks for modeling active perception tasks, that restore the PWLC property of the value function. To efficiently plan for active perception tasks, we identify and exploit the independence properties of POMDP-IR to reduce the computational cost of solving POMDP-IR (and $ρ$POMDP). We propose greedy point-based value iteration (PBVI), a new POMDP planning method that uses greedy maximization to greatly improve scalability in the action space of an active perception POMDP. Furthermore, we show that, under certain conditions, including submodularity, the value function computed using greedy PBVI is guaranteed to have bounded error with respect to the optimal value function. We establish the conditions under which the value function of an active perception POMDP is guaranteed to be submodular. Finally, we present a detailed empirical analysis on a dataset collected from a multi-camera tracking system employed in a shopping mall. Our method achieves similar performance to existing methods but at a fraction of the computational cost leading to better scalability for solving active perception tasks.

Yash Satsangi, Shimon Whiteson, Frans A. Oliehoek et al.

Automated tracking is key to many computer vision applications. However, many tracking systems struggle to perform in real-time due to the high computational cost of detecting people, especially in ultra high resolution images. We propose a new algorithm called \emph{PartiMax} that greatly reduces this cost by applying the person detector only to the relevant parts of the image. PartiMax exploits information in the particle filter to select $k$ of the $n$ candidate \emph{pixel boxes} in the image. We prove that PartiMax is guaranteed to make a near-optimal selection with error bounds that are independent of the problem size. Furthermore, empirical results on a real-life dataset show that our system runs in real-time by processing only 10\% of the pixel boxes in the image while still retaining 80\% of the original tracking performance achieved when processing all pixel boxes.

Elise van der Pol, Daniel E. Worrall, Herke van Hoof et al.

This paper introduces MDP homomorphic networks for deep reinforcement learning. MDP homomorphic networks are neural networks that are equivariant under symmetries in the joint state-action space of an MDP. Current approaches to deep reinforcement learning do not usually exploit knowledge about such structure. By building this prior knowledge into policy and value networks using an equivariance constraint, we can reduce the size of the solution space. We specifically focus on group-structured symmetries (invertible transformations). Additionally, we introduce an easy method for constructing equivariant network layers numerically, so the system designer need not solve the constraints by hand, as is typically done. We construct MDP homomorphic MLPs and CNNs that are equivariant under either a group of reflections or rotations. We show that such networks converge faster than unstructured baselines on CartPole, a grid world and Pong.

Flávia Alves, Martin Gairing, Frans A. Oliehoek et al.

The field of Human Activity Recognition (HAR) focuses on obtaining and analysing data captured from monitoring devices (e.g. sensors). There is a wide range of applications within the field; for instance, assisted living, security surveillance, and intelligent transportation. In HAR, the development of Activity Recognition models is dependent upon the data captured by these devices and the methods used to analyse them, which directly affect performance metrics. In this work, we address the issue of accurately recognising human activities using different Machine Learning (ML) techniques. We propose a new feature representation based on consecutive occurring observations and compare it against previously used feature representations using a wide range of classification methods. Experimental results demonstrate that techniques based on the proposed representation outperform the baselines and a better accuracy was achieved for both highly and less frequent actions. We also investigate how the addition of further features and their pre-processing techniques affect performance results leading to state-of-the-art accuracy on a Human Activity Recognition dataset.

Christian Muench, Frans A. Oliehoek, Dariu M. Gavrila

Traffic scenarios are inherently interactive. Multiple decision-makers predict the actions of others and choose strategies that maximize their rewards. We view these interactions from the perspective of game theory which introduces various challenges. Humans are not entirely rational, their rewards need to be inferred from real-world data, and any prediction algorithm needs to be real-time capable so that we can use it in an autonomous vehicle (AV). In this work, we present a game-theoretic method that addresses all of the points above. Compared to many existing methods used for AVs, our approach does 1) not require perfect communication, and 2) allows for individual rewards per agent. Our experiments demonstrate that these more realistic assumptions lead to qualitatively and quantitatively different reward inference and prediction of future actions that match better with expected real-world behaviour.

João P. Abrantes, Arnaldo J. Abrantes, Frans A. Oliehoek

Evolution gave rise to human and animal intelligence here on Earth. We argue that the path to developing artificial human-like-intelligence will pass through mimicking the evolutionary process in a nature-like simulation. In Nature, there are two processes driving the development of the brain: evolution and learning. Evolution acts slowly, across generations, and amongst other things, it defines what agents learn by changing their internal reward function. Learning acts fast, across one's lifetime, and it quickly updates agents' policy to maximise pleasure and minimise pain. The reward function is slowly aligned with the fitness function by evolution, however, as agents evolve the environment and its fitness function also change, increasing the misalignment between reward and fitness. It is extremely computationally expensive to replicate these two processes in simulation. This work proposes Evolution via Evolutionary Reward (EvER) that allows learning to single-handedly drive the search for policies with increasingly evolutionary fitness by ensuring the alignment of the reward function with the fitness function. In this search, EvER makes use of the whole state-action trajectories that agents go through their lifetime. In contrast, current evolutionary algorithms discard this information and consequently limit their potential efficiency at tackling sequential decision problems. We test our algorithm in two simple bio-inspired environments and show its superiority at generating more capable agents at surviving and reproducing their genes when compared with a state-of-the-art evolutionary algorithm.

Aleksander Czechowski, Frans A. Oliehoek

Decentralized online planning can be an attractive paradigm for cooperative multi-agent systems, due to improved scalability and robustness. A key difficulty of such approach lies in making accurate predictions about the decisions of other agents. In this paper, we present a trainable online decentralized planning algorithm based on decentralized Monte Carlo Tree Search, combined with models of teammates learned from previous episodic runs. By only allowing one agent to adapt its models at a time, under the assumption of ideal policy approximation, successive iterations of our method are guaranteed to improve joint policies, and eventually lead to convergence to a Nash equilibrium. We test the efficiency of the algorithm by performing experiments in several scenarios of the spatial task allocation environment introduced in [Claes et al., 2015]. We show that deep learning and convolutional neural networks can be employed to produce accurate policy approximators which exploit the spatial features of the problem, and that the proposed algorithm improves over the baseline planning performance for particularly challenging domain configurations.

Elise van der Pol, Thomas Kipf, Frans A. Oliehoek et al.

This work exploits action equivariance for representation learning in reinforcement learning. Equivariance under actions states that transitions in the input space are mirrored by equivalent transitions in latent space, while the map and transition functions should also commute. We introduce a contrastive loss function that enforces action equivariance on the learned representations. We prove that when our loss is zero, we have a homomorphism of a deterministic Markov Decision Process (MDP). Learning equivariant maps leads to structured latent spaces, allowing us to build a model on which we plan through value iteration. We show experimentally that for deterministic MDPs, the optimal policy in the abstract MDP can be successfully lifted to the original MDP. Moreover, the approach easily adapts to changes in the goal states. Empirically, we show that in such MDPs, we obtain better representations in fewer epochs compared to representation learning approaches using reconstructions, while generalizing better to new goals than model-free approaches.

Miguel Suau, Jinke He, Elena Congeduti et al.

Due to its perceptual limitations, an agent may have too little information about the state of the environment to act optimally. In such cases, it is important to keep track of the observation history to uncover hidden state. Recent deep reinforcement learning methods use recurrent neural networks (RNN) to memorize past observations. However, these models are expensive to train and have convergence difficulties, especially when dealing with high dimensional input spaces. In this paper, we propose influence-aware memory (IAM), a theoretically inspired memory architecture that tries to alleviate the training difficulties by restricting the input of the recurrent layers to those variables that influence the hidden state information. Moreover, as opposed to standard RNNs, in which every piece of information used for estimating Q values is inevitably fed back into the network for the next prediction, our model allows information to flow without being necessarily stored in the RNN's internal memory. Results indicate that, by letting the recurrent layers focus on a small fraction of the observation variables while processing the rest of the information with a feedforward neural network, we can outperform standard recurrent architectures both in training speed and policy performance. This approach also reduces runtime and obtains better scores than methods that stack multiple observations to remove partial observability.

Frans A. Oliehoek, Stefan Witwicki, Leslie P. Kaelbling

Making decisions in complex environments is a key challenge in artificial intelligence (AI). Situations involving multiple decision makers are particularly complex, leading to computational intractability of principled solution methods. A body of work in AI has tried to mitigate this problem by trying to distill interaction to its essence: how does the policy of one agent influence another agent? If we can find more compact representations of such influence, this can help us deal with the complexity, for instance by searching the space of influences rather than the space of policies. However, so far these notions of influence have been restricted in their applicability to special cases of interaction. In this paper we formalize influence-based abstraction (IBA), which facilitates the elimination of latent state factors without any loss in value, for a very general class of problems described as factored partially observable stochastic games (fPOSGs). On the one hand, this generalizes existing descriptions of influence, and thus can serve as the foundation for improvements in scalability and other insights in decision making in complex multiagent settings. On the other hand, since the presence of other agents can be seen as a generalization of single agent settings, our formulation of IBA also provides a sufficient statistic for decision making under abstraction for a single agent. We also give a detailed discussion of the relations to such previous works, identifying new insights and interpretations of these approaches. In these ways, this paper deepens our understanding of abstraction in a wide range of sequential decision making settings, providing the basis for new approaches and algorithms for a large class of problems.

Feryal Behbahani, Kyriacos Shiarlis, Xi Chen et al.

Learning from demonstration (LfD) is useful in settings where hand-coding behaviour or a reward function is impractical. It has succeeded in a wide range of problems but typically relies on manually generated demonstrations or specially deployed sensors and has not generally been able to leverage the copious demonstrations available in the wild: those that capture behaviours that were occurring anyway using sensors that were already deployed for another purpose, e.g., traffic camera footage capturing demonstrations of natural behaviour of vehicles, cyclists, and pedestrians. We propose Video to Behaviour (ViBe), a new approach to learn models of behaviour from unlabelled raw video data of a traffic scene collected from a single, monocular, initially uncalibrated camera with ordinary resolution. Our approach calibrates the camera, detects relevant objects, tracks them through time, and uses the resulting trajectories to perform LfD, yielding models of naturalistic behaviour. We apply ViBe to raw videos of a traffic intersection and show that it can learn purely from videos, without additional expert knowledge.

Frans A. Oliehoek, Rahul Savani, Jose Gallego et al.

Save for some special cases, current training methods for Generative Adversarial Networks (GANs) are at best guaranteed to converge to a `local Nash equilibrium` (LNE). Such LNEs, however, can be arbitrarily far from an actual Nash equilibrium (NE), which implies that there are no guarantees on the quality of the found generator or classifier. This paper proposes to model GANs explicitly as finite games in mixed strategies, thereby ensuring that every LNE is an NE. With this formulation, we propose a solution method that is proven to monotonically converge to a resource-bounded Nash equilibrium (RB-NE): by increasing computational resources we can find better solutions. We empirically demonstrate that our method is less prone to typical GAN problems such as mode collapse, and produces solutions that are less exploitable than those produced by GANs and MGANs, and closely resemble theoretical predictions about NEs.

Sammie Katt, Frans A. Oliehoek, Christopher Amato

The POMDP is a powerful framework for reasoning under outcome and information uncertainty, but constructing an accurate POMDP model is difficult. Bayes-Adaptive Partially Observable Markov Decision Processes (BA-POMDPs) extend POMDPs to allow the model to be learned during execution. BA-POMDPs are a Bayesian RL approach that, in principle, allows for an optimal trade-off between exploitation and exploration. Unfortunately, BA-POMDPs are currently impractical to solve for any non-trivial domain. In this paper, we extend the Monte-Carlo Tree Search method POMCP to BA-POMDPs and show that the resulting method, which we call BA-POMCP, is able to tackle problems that previous solution methods have been unable to solve. Additionally, we introduce several techniques that exploit the BA-POMDP structure to improve the efficiency of BA-POMCP along with proof of their convergence.

Frans A. Oliehoek, Rahul Savani, Jose Gallego-Posada et al.

Generative Adversarial Networks (GAN) have become one of the most successful frameworks for unsupervised generative modeling. As GANs are difficult to train much research has focused on this. However, very little of this research has directly exploited game-theoretic techniques. We introduce Generative Adversarial Network Games (GANGs), which explicitly model a finite zero-sum game between a generator ($G$) and classifier ($C$) that use mixed strategies. The size of these games precludes exact solution methods, therefore we define resource-bounded best responses (RBBRs), and a resource-bounded Nash Equilibrium (RB-NE) as a pair of mixed strategies such that neither $G$ or $C$ can find a better RBBR. The RB-NE solution concept is richer than the notion of `local Nash equilibria' in that it captures not only failures of escaping local optima of gradient descent, but applies to any approximate best response computations, including methods with random restarts. To validate our approach, we solve GANGs with the Parallel Nash Memory algorithm, which provably monotonically converges to an RB-NE. We compare our results to standard GAN setups, and demonstrate that our method deals well with typical GAN problems such as mode collapse, partial mode coverage and forgetting.

Auke J. Wiggers, Frans A. Oliehoek, Diederik M. Roijers

Zero-sum stochastic games provide a rich model for competitive decision making. However, under general forms of state uncertainty as considered in the Partially Observable Stochastic Game (POSG), such decision making problems are still not very well understood. This paper makes a contribution to the theory of zero-sum POSGs by characterizing structure in their value function. In particular, we introduce a new formulation of the value function for zs-POSGs as a function of the "plan-time sufficient statistics" (roughly speaking the information distribution in the POSG), which has the potential to enable generalization over such information distributions. We further delineate this generalization capability by proving a structural result on the shape of value function: it exhibits concavity and convexity with respect to appropriately chosen marginals of the statistic space. This result is a key pre-cursor for developing solution methods that may be able to exploit such structure. Finally, we show how these results allow us to reduce a zs-POSG to a "centralized" model with shared observations, thereby transferring results for the latter, narrower class, to games with individual (private) observations.

Yash Satsangi, Shimon Whiteson, Frans A. Oliehoek

Submodular function maximization finds application in a variety of real-world decision-making problems. However, most existing methods, based on greedy maximization, assume it is computationally feasible to evaluate F, the function being maximized. Unfortunately, in many realistic settings F is too expensive to evaluate exactly even once. We present probably approximately correct greedy maximization, which requires access only to cheap anytime confidence bounds on F and uses them to prune elements. We show that, with high probability, our method returns an approximately optimal set. We propose novel, cheap confidence bounds for conditional entropy, which appears in many common choices of F and for which it is difficult to find unbiased or bounded estimates. Finally, results on a real-world dataset from a multi-camera tracking system in a shopping mall demonstrate that our approach performs comparably to existing methods, but at a fraction of the computational cost.

Athirai A. Irissappane, Frans A. Oliehoek, Jie Zhang

In multiagent e-marketplaces, buying agents need to select good sellers by querying other buyers (called advisors). Partially Observable Markov Decision Processes (POMDPs) have shown to be an effective framework for optimally selecting sellers by selectively querying advisors. However, current solution methods do not scale to hundreds or even tens of agents operating in the e-market. In this paper, we propose the Mixture of POMDP Experts (MOPE) technique, which exploits the inherent structure of trust-based domains, such as the seller selection problem in e-markets, by aggregating the solutions of smaller sub-POMDPs. We propose a number of variants of the MOPE approach that we analyze theoretically and empirically. Experiments show that MOPE can scale up to a hundred agents thereby leveraging the presence of more advisors to significantly improve buyer satisfaction.

Philipp Robbel, Frans A. Oliehoek, Mykel J. Kochenderfer

Many exact and approximate solution methods for Markov Decision Processes (MDPs) attempt to exploit structure in the problem and are based on factorization of the value function. Especially multiagent settings, however, are known to suffer from an exponential increase in value component sizes as interactions become denser, meaning that approximation architectures are restricted in the problem sizes and types they can handle. We present an approach to mitigate this limitation for certain types of multiagent systems, exploiting a property that can be thought of as "anonymous influence" in the factored MDP. Anonymous influence summarizes joint variable effects efficiently whenever the explicit representation of variable identity in the problem can be avoided. We show how representational benefits from anonymity translate into computational efficiencies, both for general variable elimination in a factor graph but in particular also for the approximate linear programming solution to factored MDPs. The latter allows to scale linear programming to factored MDPs that were previously unsolvable. Our results are shown for the control of a stochastic disease process over a densely connected graph with 50 nodes and 25 agents.

Joris Scharpff, Diederik M. Roijers, Frans A. Oliehoek et al.

In cooperative multi-agent sequential decision making under uncertainty, agents must coordinate to find an optimal joint policy that maximises joint value. Typical algorithms exploit additive structure in the value function, but in the fully-observable multi-agent MDP setting (MMDP) such structure is not present. We propose a new optimal solver for transition-independent MMDPs, in which agents can only affect their own state but their reward depends on joint transitions. We represent these dependencies compactly in conditional return graphs (CRGs). Using CRGs the value of a joint policy and the bounds on partially specified joint policies can be efficiently computed. We propose CoRe, a novel branch-and-bound policy search algorithm building on CRGs. CoRe typically requires less runtime than the available alternatives and finds solutions to problems previously unsolvable.