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Markov $\alpha$-Potential Games: Equilibrium Approximation and Regret Analysis

arXiv.org Artificial Intelligence

This paper proposes a new notion of Markov ฮฑ-potential games to study Markov games. Two important classes of practically significant Markov games, Markov congestion games and the perturbed Markov team games, are analyzed in this framework of Markov ฮฑ-potential games, with explicit characterization of the upper bound for ฮฑ and its relation to game parameters. Moreover, any maximizer of the ฮฑ-potential function is shown to be an ฮฑ-stationary Nash equilibrium of the game. Furthermore, two algorithms for the Nash regret analysis, namely the projected gradient-ascent algorithm and the sequential maximum improvement algorithm, are presented and corroborated by numerical experiments. Key words: Markov ฮฑ-potential games; Markov potential games; Multi-agent reinforcement learning; Nash-regret; Markov congestion games; Perturbed Markov team games; Projected gradient-ascent algorithm; Sequential maximum improvement.


Independent and Decentralized Learning in Markov Potential Games

arXiv.org Artificial Intelligence

We propose a multi-agent reinforcement learning dynamics, and analyze its convergence in infinite-horizon discounted Markov potential games. We focus on the independent and decentralized setting, where players do not have knowledge of the game model and cannot coordinate. In each stage, players update their estimate of Q-function that evaluates their total contingent payoff based on the realized one-stage reward in an asynchronous manner. Then, players independently update their policies by incorporating an optimal one-stage deviation strategy based on the estimated Q-function. A key feature of the learning dynamics is that the Q-function estimates are updated at a faster timescale than the policies. We prove that the policies induced by our learning dynamics converge to the set of stationary Nash equilibria in Markov potential games with probability 1. Our results highlight the efficacy of simple learning dynamics in reaching to the set of stationary Nash equilibrium even in environments with minimal information available.


Price Interpretability of Prediction Markets: A Convergence Analysis

arXiv.org Artificial Intelligence

Prediction markets are long known for prediction accuracy. This study systematically explores the fundamental properties of prediction markets, addressing questions about their information aggregation process and the factors contributing to their remarkable efficacy. We propose a novel multivariate utility (MU) based mechanism that unifies several existing automated market-making schemes. Using this mechanism, we establish the convergence results for markets comprised of risk-averse traders who have heterogeneous beliefs and repeatedly interact with the market maker. We demonstrate that the resulting limiting wealth distribution aligns with the Pareto efficient frontier defined by the utilities of all market participants. With the help of this result, we establish analytical and numerical results for the limiting price in different market models. Specifically, we show that the limiting price converges to the geometric mean of agent beliefs in exponential utility-based markets. In risk-measure-based markets, we construct a family of risk measures that satisfy the convergence criteria and prove that the price can converge to a unique level represented by the weighted power mean of agent beliefs. In broader markets with Constant Relative Risk Aversion (CRRA) utilities, we reveal that the limiting price can be characterized by systems of equations that encapsulate agent beliefs, risk parameters, and wealth. Despite the potential impact of traders' trading sequences on the limiting price, we establish a price invariance result for markets with a large trader population. Using this result, we propose an efficient approximation scheme for the limiting price.


Analysing Factorizations of Action-Value Networks for Cooperative Multi-Agent Reinforcement Learning

arXiv.org Artificial Intelligence

Recent years have seen the application of deep reinforcement learning techniques to cooperative multi-agent systems, with great empirical success. However, given the lack of theoretical insight, it remains unclear what the employed neural networks are learning, or how we should enhance their learning power to address the problems on which they fail. In this work, we empirically investigate the learning power of various network architectures on a series of one-shot games. Despite their simplicity, these games capture many of the crucial problems that arise in the multi-agent setting, such as an exponential number of joint actions or the lack of an explicit coordination mechanism. Our results extend those in [4] and quantify how well various approaches can represent the requisite value functions, and help us identify the reasons that can impede good performance, like sparsity of the values or too tight coordination requirements.


Probable Approximate Coordination

arXiv.org Artificial Intelligence

We study the problem of how to coordinate the actions of independent agents in a distributed system where message arrival times are unbounded, but are determined by an exponential probability distribution. Asynchronous protocols executed in such a model are guaranteed to succeed with probability 1. We demonstrate a case in which the best asynchronous protocol can be improved on significantly. Specifically, we focus on the task of performing actions by different agents in a linear temporal order -- a problem known in the literature as Ordered Response. In asynchronous systems, ensuring such an ordering requires the construction of a message chain that passes through each acting agent, in order. Solving Ordered Response in this way in our model will terminate in time that grows linearly in the number of participating agents $n$, in expectation. We show that relaxing the specification slightly allows for a significant saving in time. Namely, if Ordered Response should be guaranteed with high probability (arbitrarily close to 1), it is possible to significantly shorten the expected execution time of the protocol. We present two protocols that adhere to the relaxed specification. One of our protocols executes exponentially faster than a message chain, when the number of participating agents $n$ is large, while the other is roughly quadratically faster. For small values of $n$, it is also possible to achieve similar results by using a hybrid protocol.


Reliable and Efficient Data Collection in UAV-based IoT Networks

arXiv.org Artificial Intelligence

Internet of Things (IoT) involves sensors for monitoring and wireless networks for efficient communication. However, resource-constrained IoT devices and limitations in existing wireless technologies hinder its full potential. Integrating Unmanned Aerial Vehicles (UAVs) into IoT networks can address some challenges by expanding its' coverage, providing security, and bringing computing closer to IoT devices. Nevertheless, effective data collection in UAV-assisted IoT networks is hampered by factors, including dynamic UAV behavior, environmental variables, connectivity instability, and security considerations. In this survey, we first explore UAV-based IoT networks, focusing on communication and networking aspects. Next, we cover various UAV-based data collection methods their advantages and disadvantages, followed by a discussion on performance metrics for data collection. As this article primarily emphasizes reliable and efficient data collection in UAV-assisted IoT networks, we briefly discuss existing research on data accuracy and consistency, network connectivity, and data security and privacy to provide insights into reliable data collection. Additionally, we discuss efficient data collection strategies in UAV-based IoT networks, covering trajectory and path planning, collision avoidance, sensor network clustering, data aggregation, UAV swarm formations, and artificial intelligence for optimization. We also present two use cases of UAVs as a service for enhancing data collection reliability and efficiency. Finally, we discuss future challenges in data collection for UAV-assisted IoT networks.


AI Agent as Urban Planner: Steering Stakeholder Dynamics in Urban Planning via Consensus-based Multi-Agent Reinforcement Learning

arXiv.org Artificial Intelligence

In urban planning, land use readjustment plays a pivotal role in aligning land use configurations with the current demands for sustainable urban development. However, present-day urban planning practices face two main issues. Firstly, land use decisions are predominantly dependent on human experts. Besides, while resident engagement in urban planning can promote urban sustainability and livability, it is challenging to reconcile the diverse interests of stakeholders. To address these challenges, we introduce a Consensus-based Multi-Agent Reinforcement Learning framework for real-world land use readjustment. This framework serves participatory urban planning, allowing diverse intelligent agents as stakeholder representatives to vote for preferred land use types. Within this framework, we propose a novel consensus mechanism in reward design to optimize land utilization through collective decision making. To abstract the structure of the complex urban system, the geographic information of cities is transformed into a spatial graph structure and then processed by graph neural networks. Comprehensive experiments on both traditional top-down planning and participatory planning methods from real-world communities indicate that our computational framework enhances global benefits and accommodates diverse interests, leading to improved satisfaction across different demographic groups. By integrating Multi-Agent Reinforcement Learning, our framework ensures that participatory urban planning decisions are more dynamic and adaptive to evolving community needs and provides a robust platform for automating complex real-world urban planning processes.


Difference Rewards Policy Gradients

arXiv.org Artificial Intelligence

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.


Towards A Natural Language Interface for Flexible Multi-Agent Task Assignment

arXiv.org Artificial Intelligence

Task assignment and scheduling algorithms are powerful tools for autonomously coordinating large teams of robotic or AI agents. However, the decisions these system make often rely on components designed by domain experts, which can be difficult for non-technical end-users to understand or modify to their own ends. In this paper we propose a preliminary design for a flexible natural language interface for a task assignment system. The goal of our approach is both to grant users more control over a task assignment system's decision process, as well as render these decisions more transparent. Users can direct the task assignment system via natural language commands, which are applied as constraints to a mixed-integer linear program (MILP) using a large language model (LLM). Additionally, our proposed system can alert users to potential issues with their commands, and engage them in a corrective dialogue in order to find a viable solution. We conclude with a description of our planned user-evaluation in the simulated environment Overcooked and describe next steps towards developing a flexible and transparent task allocation system.


RAMP: A Benchmark for Evaluating Robotic Assembly Manipulation and Planning

arXiv.org Artificial Intelligence

We introduce RAMP, an open-source robotics benchmark inspired by real-world industrial assembly tasks. RAMP consists of beams that a robot must assemble into specified goal configurations using pegs as fasteners. As such, it assesses planning and execution capabilities, and poses challenges in perception, reasoning, manipulation, diagnostics, fault recovery, and goal parsing. RAMP has been designed to be accessible and extensible. Parts are either 3D printed or otherwise constructed from materials that are readily obtainable. The design of parts and detailed instructions are publicly available. In order to broaden community engagement, RAMP incorporates fixtures such as April Tags which enable researchers to focus on individual sub-tasks of the assembly challenge if desired. We provide a full digital twin as well as rudimentary baselines to enable rapid progress. Our vision is for RAMP to form the substrate for a community-driven endeavour that evolves as capability matures.