Optimal allocation of agricultural water in the event of droughts is an important global problem. In addressing this problem, many aspects, including the welfare of farmers, the economy, and the environment, must be considered. Under this backdrop, our work focuses on several resource-matching problems accounting for agents with multi-crop portfolios, geographic constraints, and fairness. First, we address a matching problem where the goal is to maximize a welfare function in two-sided markets where buyers' requirements and sellers' supplies are represented by value functions that assign prices (or costs) to specified volumes of water. For the setting where the value functions satisfy certain monotonicity properties, we present an efficient algorithm that maximizes a social welfare function. When there are minimum water requirement constraints, we present a randomized algorithm which ensures that the constraints are satisfied in expectation. For a single seller--multiple buyers setting with fairness constraints, we design an efficient algorithm that maximizes the minimum level of satisfaction of any buyer. We also present computational complexity results that highlight the limits on the generalizability of our results. We evaluate the algorithms developed in our work with experiments on both real-world and synthetic data sets with respect to drought severity, value functions, and seniority of agents.

Trajectory planning is a fundamental problem in robotics. It facilitates a wide range of applications in navigation and motion planning, control, and multi-agent coordination. Trajectory planning is a difficult problem due to its computational complexity and real-world environment complexity with uncertainty, non-linearity, and real-time requirements. The multi-agent trajectory planning problem adds another dimension of difficulty due to inter-agent interaction. Existing solutions are either search-based or optimization-based approaches with simplified assumptions of environment, limited planning speed, and limited scalability in the number of agents. In this work, we make the first attempt to reformulate single agent and multi-agent trajectory planning problem as query problems over an implicit neural representation of trajectories. We formulate such implicit representation as Neural Trajectory Models (NTM) which can be queried to generate nearly optimal trajectory in complex environments. We conduct experiments in simulation environments and demonstrate that NTM can solve single-agent and multi-agent trajectory planning problems. In the experiments, NTMs achieve (1) sub-millisecond panning time using GPUs, (2) almost avoiding all environment collision, (3) almost avoiding all inter-agent collision, and (4) generating almost shortest paths. We also demonstrate that the same NTM framework can also be used for trajectories correction and multi-trajectory conflict resolution refining low quality and conflicting multi-agent trajectories into nearly optimal solutions efficiently. (Open source code will be available at https://github.com/laser2099/neural-trajectory-model)

Markov Games (MG) is an important model for Multi-Agent Reinforcement Learning (MARL). It was long believed that the "curse of multi-agents" (i.e., the algorithmic performance drops exponentially with the number of agents) is unavoidable until several recent works (Daskalakis et al., 2023; Cui et al., 2023; Wang et al., 2023. While these works did resolve the curse of multi-agents, when the state spaces are prohibitively large and (linear) function approximations are deployed, they either had a slower convergence rate of $O(T^{-1/4})$ or brought a polynomial dependency on the number of actions $A_{\max}$ -- which is avoidable in single-agent cases even when the loss functions can arbitrarily vary with time (Dai et al., 2023). This paper first refines the `AVLPR` framework by Wang et al. (2023), with an insight of *data-dependent* (i.e., stochastic) pessimistic estimation of the sub-optimality gap, allowing a broader choice of plug-in algorithms. When specialized to MGs with independent linear function approximations, we propose novel *action-dependent bonuses* to cover occasionally extreme estimation errors. With the help of state-of-the-art techniques from the single-agent RL literature, we give the first algorithm that tackles the curse of multi-agents, attains the optimal $O(T^{-1/2})$ convergence rate, and avoids $\text{poly}(A_{\max})$ dependency simultaneously.

Reward allocation, also known as the credit assignment problem, has been an important topic in economics, engineering, and machine learning. An important concept in credit assignment is the core, which is the set of stable allocations where no agent has the motivation to deviate from the grand coalition. In this paper, we consider the stable allocation learning problem of stochastic cooperative games, where the reward function is characterised as a random variable with an unknown distribution. Given an oracle that returns a stochastic reward for an enquired coalition each round, our goal is to learn the expected core, that is, the set of allocations that are stable in expectation. Within the class of strictly convex games, we present an algorithm named \texttt{Common-Points-Picking} that returns a stable allocation given a polynomial number of samples, with high probability. The analysis of our algorithm involves the development of several new results in convex geometry, including an extension of the separation hyperplane theorem for multiple convex sets, and may be of independent interest.

In the field of Multi-Agent Systems (MAS), known for their openness, dynamism, and cooperative nature, the ability to trust the resources and services of other agents is crucial. Trust, in this setting, is the reliance and confidence an agent has in the information, behaviors, intentions, truthfulness, and capabilities of others within the system. Our paper introduces a new graphical approach that utilizes factor graphs to represent the interdependent behaviors and trustworthiness among agents. This includes modeling the behavior of robots as a trajectory of actions using a Gaussian process factor graph, which accounts for smoothness, obstacle avoidance, and trust-related factors. Our method for evaluating trust is decentralized and considers key interdependent sub-factors such as proximity safety, consistency, and cooperation. The overall system comprises a network of factor graphs that interact through trust-related factors and employs a Bayesian inference method to dynamically assess trust-based decisions with informed consent. The effectiveness of this method is validated via simulations and empirical tests with autonomous robots navigating unsignalized intersections.

In multi-agent settings with mixed incentives, methods developed for zero-sum games have been shown to lead to detrimental outcomes. To address this issue, opponent shaping (OS) methods explicitly learn to influence the learning dynamics of co-players and empirically lead to improved individual and collective outcomes. However, OS methods have only been evaluated in low-dimensional environments due to the challenges associated with estimating higher-order derivatives or scaling model-free meta-learning. Alternative methods that scale to more complex settings either converge to undesirable solutions or rely on unrealistic assumptions about the environment or co-players. In this paper, we successfully scale an OS-based approach to general-sum games with temporally-extended actions and long-time horizons for the first time. After analysing the representations of the meta-state and history used by previous algorithms, we propose a simplified version called Shaper. We show empirically that Shaper leads to improved individual and collective outcomes in a range of challenging settings from literature. We further formalize a technique previously implicit in the literature, and analyse its contribution to opponent shaping. We show empirically that this technique is helpful for the functioning of prior methods in certain environments. Lastly, we show that previous environments, such as the CoinGame, are inadequate for analysing temporally-extended general-sum interactions.

An urban planner might design the spatial layout of transportation amenities so as to improve accessibility for underserved communities -- a fairness objective. However, implementing such a design might trigger processes of neighborhood change that change who benefits from these amenities in the long term. If so, has the planner really achieved their fairness objective? Can algorithmic decision-making anticipate second order effects? In this paper, we take a step in this direction by formulating processes of neighborhood change as instances of no-regret dynamics; a collective learning process in which a set of strategic agents rapidly reach a state of approximate equilibrium. We mathematize concepts of neighborhood change to model the incentive structures impacting individual dwelling-site decision-making. Our model accounts for affordability, access to relevant transit amenities, community ties, and site upkeep. We showcase our model with computational experiments that provide semi-quantitative insights on the spatial economics of neighborhood change, particularly on the influence of residential zoning policy and the placement of transit amenities.

Deceptive path planning (DPP) is the problem of designing a path that hides its true goal from an outside observer. Existing methods for DPP rely on unrealistic assumptions, such as global state observability and perfect model knowledge, and are typically problem-specific, meaning that even minor changes to a previously solved problem can force expensive computation of an entirely new solution. Given these drawbacks, such methods do not generalize to unseen problem instances, lack scalability to realistic problem sizes, and preclude both on-the-fly tunability of deception levels and real-time adaptivity to changing environments. In this paper, we propose a reinforcement learning (RL)-based scheme for training policies to perform DPP over arbitrary weighted graphs that overcomes these issues. The core of our approach is the introduction of a local perception model for the agent, a new state space representation distilling the key components of the DPP problem, the use of graph neural network-based policies to facilitate generalization and scaling, and the introduction of new deception bonuses that translate the deception objectives of classical methods to the RL setting. Through extensive experimentation we show that, without additional fine-tuning, at test time the resulting policies successfully generalize, scale, enjoy tunable levels of deception, and adapt in real-time to changes in the environment.

Co-creativity in music refers to two or more musicians or musical agents interacting with one another by composing or improvising music. However, this is a very subjective process and each musician has their own preference as to which improvisation is better for some context. In this paper, we aim to create a measure based on total information flow to quantitatively evaluate the co-creativity process in music. In other words, our measure is an indication of how "good" a creative musical process is. Our main hypothesis is that a good musical creation would maximize information flow between the participants captured by music voices recorded in separate tracks. We propose a method to compute the information flow using pre-trained generative models as entropy estimators. We demonstrate how our method matches with human perception using a qualitative study.

Simulation-to-reality (sim-to-real) transfer is a fundamental problem for robot learning. Domain Randomization, which adds randomization during training, is a powerful technique that effectively addresses the sim-to-real gap. However, the noise in observations makes learning significantly harder. Recently, studies have shown that employing a teacher-student learning paradigm can accelerate training in randomized environments. Learned with privileged information, a teacher agent can instruct the student agent to operate in noisy environments. However, this approach is often not sample efficient as the experience collected by the teacher is discarded completely when training the student, wasting information revealed by the environment. In this work, we extend the teacher-student learning paradigm by proposing a sample efficient learning framework termed Learn to Teach (L2T) that recycles experience collected by the teacher agent. We observe that the dynamics of the environments for both agents remain unchanged, and the state space of the teacher is coupled with the observation space of the student. We show that a single-loop algorithm can train both the teacher and student agents under both Reinforcement Learning and Inverse Reinforcement Learning contexts. We implement variants of our methods, conduct experiments on the MuJoCo benchmark, and apply our methods to the Cassie robot locomotion problem. Extensive experiments show that our method achieves competitive performance while only requiring environmental interaction with the teacher.