In fair division of a connected graph $G = (V, E)$, each of $n$ agents receives a share of $G$'s vertex set $V$. These shares partition $V$, with each share required to induce a connected subgraph. Agents use their own valuation functions to determine the non-negative numerical values of the shares, which determine whether the allocation is fair in some specified sense. We introduce forbidden substructures called graph cutsets, which block divisions that are fair in the EF1 (envy-free up to one item) sense by cutting the graph into "too many pieces". Two parameters - gap and valence - determine blocked values of $n$. If $G$ guarantees connected EF1 allocations for $n$ agents with valuations that are CA (common and additive), then $G$ contains no elementary cutset of gap $k \ge 2$ and valence in the interval $\[n - k + 1, n - 1\]$. If $G$ guarantees connected EF1 allocations for $n$ agents with valuations in the broader CM (common and monotone) class, then $G$ contains no cutset of gap $k \ge 2$ and valence in the interval $\[n - k + 1, n - 1\]$. These results rule out the existence of connected EF1 allocations in a variety of situations. For some graphs $G$ we can, with help from some new positive results, pin down $G$'s spectrum - the list of exactly which values of $n$ do/do not guarantee connected EF1 allocations. Examples suggest a conjectured common spectral pattern for all graphs. Further, we show that it is NP-hard to determine whether a graph admits a cutset. We also provide an example of a (non-traceable) graph on eight vertices that has no cutsets of gap $\ge 2$ at all, yet fails to guarantee connected EF1 allocations for three agents with CA preferences.

Offline RL (Levine et al., 2020), also known as batch RL, addresses the challenge of learning a near-optimal policy using offline datasets collected a priori, without further interactions with an environment. Fueled by the cost-effectiveness of utilizing pre-collected datasets compared to real-time explorations, offline RL has received increasing attention. However, the performance of offline RL crucially depends on the quality of offline datasets due to the lack of additional interactions with the environment, where the quality is determined by how thoroughly the state-action space is explored during data collection. Encouragingly, recent research (Li et al., 2022; Rashidinejad et al., 2021; Shi et al., 2022; Xie et al., 2021b) indicates that being more conservative on unseen state-action pairs, known as the principle of pessimism, enables learning of a near-optimal policy even with partial coverage of the state-action space, as long as the distribution of datasets encompasses the trajectory of the optimal policy. However, acquiring high-quality datasets that have good coverage of the optimal policy poses challenges because it requires the state-action visitation distribution induced by a behavior policy employed for data collection to be very close to the optimal policy. Alternatively, multiple datasets can be merged into one dataset to supplement insufficient coverage of one other, but this may be impractical when offline datasets are scattered and cannot be easily shared due to privacy and communication constraints.

There is increasing focus on adapting predictive models into agent-like systems, most notably AI assistants based on language models. We outline two structural reasons for why these models can fail when turned into agents. First, we discuss auto-suggestive delusions. Prior work has shown theoretically that models fail to imitate agents that generated the training data if the agents relied on hidden observations: the hidden observations act as confounding variables, and the models treat actions they generate as evidence for nonexistent observations. Second, we introduce and formally study a related, novel limitation: predictor-policy incoherence. When a model generates a sequence of actions, the model's implicit prediction of the policy that generated those actions can serve as a confounding variable. The result is that models choose actions as if they expect future actions to be suboptimal, causing them to be overly conservative. We show that both of those failures are fixed by including a feedback loop from the environment, that is, re-training the models on their own actions. We give simple demonstrations of both limitations using Decision Transformers and confirm that empirical results agree with our conceptual and formal analysis. Our treatment provides a unifying view of those failure modes, and informs the question of why fine-tuning offline learned policies with online learning makes them more effective.

Learning in general-sum games often yields collectively sub-optimal results. Addressing this, opponent shaping (OS) methods actively guide the learning processes of other agents, empirically leading to improved individual and group performances in many settings. Early OS methods use higher-order derivatives to shape the learning of co-players, making them unsuitable for shaping multiple learning steps. Follow-up work, Model-free Opponent Shaping (M-FOS), addresses these by reframing the OS problem as a meta-game. In contrast to early OS methods, there is little theoretical understanding of the M-FOS framework. Providing theoretical guarantees for M-FOS is hard because A) there is little literature on theoretical sample complexity bounds for meta-reinforcement learning B) M-FOS operates in continuous state and action spaces, so theoretical analysis is challenging. In this work, we present R-FOS, a tabular version of M-FOS that is more suitable for theoretical analysis. R-FOS discretises the continuous meta-game MDP into a tabular MDP. Within this discretised MDP, we adapt the $R_{max}$ algorithm, most prominently used to derive PAC-bounds for MDPs, as the meta-learner in the R-FOS algorithm. We derive a sample complexity bound that is exponential in the cardinality of the inner state and action space and the number of agents. Our bound guarantees that, with high probability, the final policy learned by an R-FOS agent is close to the optimal policy, apart from a constant factor. Finally, we investigate how R-FOS's sample complexity scales in the size of state-action space. Our theoretical results on scaling are supported empirically in the Matching Pennies environment.

Mean-field reinforcement learning has become a popular theoretical framework for efficiently approximating large-scale multi-agent reinforcement learning (MARL) problems exhibiting symmetry. However, questions remain regarding the applicability of mean-field approximations: in particular, their approximation accuracy of real-world systems and conditions under which they become computationally tractable. We establish explicit finite-agent bounds for how well the MFG solution approximates the true $N$-player game for two popular mean-field solution concepts. Furthermore, for the first time, we establish explicit lower bounds indicating that MFGs are poor or uninformative at approximating $N$-player games assuming only Lipschitz dynamics and rewards. Finally, we analyze the computational complexity of solving MFGs with only Lipschitz properties and prove that they are in the class of \textsc{PPAD}-complete problems conjectured to be intractable, similar to general sum $N$ player games. Our theoretical results underscore the limitations of MFGs and complement and justify existing work by proving difficulty in the absence of common theoretical assumptions.

We study the sample complexity of reinforcement learning (RL) in Mean-Field Games (MFGs) with model-based function approximation that requires strategic exploration to find a Nash Equilibrium policy. We introduce the Partial Model-Based Eluder Dimension (P-MBED), a more effective notion to characterize the model class complexity. Notably, P-MBED measures the complexity of the single-agent model class converted from the given mean-field model class, and potentially, can be exponentially lower than the MBED proposed by \citet{huang2023statistical}. We contribute a model elimination algorithm featuring a novel exploration strategy and establish sample complexity results polynomial w.r.t.~P-MBED. Crucially, our results reveal that, under the basic realizability and Lipschitz continuity assumptions, \emph{learning Nash Equilibrium in MFGs is no more statistically challenging than solving a logarithmic number of single-agent RL problems}. We further extend our results to Multi-Type MFGs, generalizing from conventional MFGs and involving multiple types of agents. This extension implies statistical tractability of a broader class of Markov Games through the efficacy of mean-field approximation. Finally, inspired by our theoretical algorithm, we present a heuristic approach with improved computational efficiency and empirically demonstrate its effectiveness.

We establish that in distributed optimization, the prevalent strategy of minimizing the second-largest eigenvalue modulus (SLEM) of the averaging matrix for selecting communication weights, while optimal for existing theoretical performance bounds, is generally not optimal regarding the exact worst-case performance of the algorithms. This exact performance can be computed using the Performance Estimation Problem (PEP) approach. We thus rely on PEP to formulate an optimization problem that determines the optimal communication weights for a distributed optimization algorithm deployed on a specified undirected graph. Our results show that the optimal weights can outperform the weights minimizing the second-largest eigenvalue modulus (SLEM) of the averaging matrix. This suggests that the SLEM is not the best characterization of weighted network performance for decentralized optimization. Additionally, we explore and compare alternative heuristics for weight selection in distributed optimization.

Various robots, rovers, drones, and other agents of mass-produced products are expected to encounter scenes where they intersect and collaborate in the near future. In such multi-agent systems, individual identification and communication play crucial roles. In this paper, we explore camera-based visible light communication using event cameras to tackle this problem. An event camera captures the events occurring in regions with changes in brightness and can be utilized as a receiver for visible light communication, leveraging its high temporal resolution. Generally, agents with identical appearances in mass-produced products are visually indistinguishable when using conventional CMOS cameras. Therefore, linking visual information with information acquired through conventional radio communication is challenging. We empirically demonstrate the advantages of a visible light communication system employing event cameras and LEDs for visual individual identification over conventional CMOS cameras with ArUco marker recognition. In the simulation, we also verified scenarios where our event camera-based visible light communication outperforms conventional radio communication in situations with visually indistinguishable multi-agents. Finally, our newly implemented multi-agent system verifies its functionality through physical robot experiments.

When humans and autonomous systems operate together as what we refer to as a hybrid team, we of course wish to ensure the team operates successfully and effectively. We refer to team members as agents. In our proposed framework, we address the case of hybrid teams in which, at any time, only one team member (the control agent) is authorized to act as control for the team. To determine the best selection of a control agent, we propose the addition of an AI manager (via Reinforcement Learning) which learns as an outside observer of the team. The manager learns a model of behavior linking observations of agent performance and the environment/world the team is operating in, and from these observations makes the most desirable selection of a control agent. We restrict the manager task by introducing a set of constraints. The manager constraints indicate acceptable team operation, so a violation occurs if the team enters a condition which is unacceptable and requires manager intervention. To ensure minimal added complexity or potential inefficiency for the team, the manager should attempt to minimize the number of times the team reaches a constraint violation and requires subsequent manager intervention. Therefore our manager is optimizing its selection of authorized agents to boost overall team performance while minimizing the frequency of manager intervention. We demonstrate our manager performance in a simulated driving scenario representing the case of a hybrid team of agents composed of a human driver and autonomous driving system. We perform experiments for our driving scenario with interfering vehicles, indicating the need for collision avoidance and proper speed control. Our results indicate a positive impact of our manager, with some cases resulting in increased team performance up to ~187% that of the best solo agent performance.

Existing approaches to fairness in stochastic multi-armed bandits (MAB) primarily focus on exposure guarantee to individual arms. When arms are naturally grouped by certain attribute(s), we propose Bi-Level Fairness, which considers two levels of fairness. At the first level, Bi-Level Fairness guarantees a certain minimum exposure to each group. To address the unbalanced allocation of pulls to individual arms within a group, we consider meritocratic fairness at the second level, which ensures that each arm is pulled according to its merit within the group. Our work shows that we can adapt a UCB-based algorithm to achieve a Bi-Level Fairness by providing (i) anytime Group Exposure Fairness guarantees and (ii) ensuring individual-level Meritocratic Fairness within each group. We first show that one can decompose regret bounds into two components: (a) regret due to anytime group exposure fairness and (b) regret due to meritocratic fairness within each group. Our proposed algorithm BF-UCB balances these two regrets optimally to achieve the upper bound of $O(\sqrt{T})$ on regret; $T$ being the stopping time. With the help of simulated experiments, we further show that BF-UCB achieves sub-linear regret; provides better group and individual exposure guarantees compared to existing algorithms; and does not result in a significant drop in reward with respect to UCB algorithm, which does not impose any fairness constraint.