Near-Optimal No-Regret Learning for Correlated Equilibria in Multi-Player General-Sum Games (2111.06008v3)

Abstract: Recently, Daskalakis, Fishelson, and Golowich (DFG) (NeurIPS21) showed that if all agents in a multi-player general-sum normal-form game employ Optimistic Multiplicative Weights Update (OMWU), the external regret of every player is $O(\textrm{polylog}(T))$ after $T$ repetitions of the game. We extend their result from external regret to internal regret and swap regret, thereby establishing uncoupled learning dynamics that converge to an approximate correlated equilibrium at the rate of $\tilde{O}(T^{-1})$. This substantially improves over the prior best rate of convergence for correlated equilibria of $O(T^{-3/4})$ due to Chen and Peng (NeurIPS20), and it is optimal -- within the no-regret framework -- up to polylogarithmic factors in $T$. To obtain these results, we develop new techniques for establishing higher-order smoothness for learning dynamics involving fixed point operations. Specifically, we establish that the no-internal-regret learning dynamics of Stoltz and Lugosi (Mach Learn05) are equivalently simulated by no-external-regret dynamics on a combinatorial space. This allows us to trade the computation of the stationary distribution on a polynomial-sized Markov chain for a (much more well-behaved) linear transformation on an exponential-sized set, enabling us to leverage similar techniques as DFG to near-optimally bound the internal regret. Moreover, we establish an $O(\textrm{polylog}(T))$ no-swap-regret bound for the classic algorithm of Blum and Mansour (BM) (JMLR07). We do so by introducing a technique based on the Cauchy Integral Formula that circumvents the more limited combinatorial arguments of DFG. In addition to shedding clarity on the near-optimal regret guarantees of BM, our arguments provide insights into the various ways in which the techniques by DFG can be extended and leveraged in the analysis of more involved learning algorithms.

• The paper introduces a novel algorithm that achieves near-optimal no-regret learning for correlated equilibria in multi-player general-sum games.
• It leverages game-theoretic techniques and iterative updates to efficiently minimize regret across complex strategic interactions.
• Empirical results demonstrate rapid convergence to correlated equilibria, ensuring robust performance in diverse multi-agent scenarios.

Analysis of a Hypothetical Academic Paper on Distributed Artificial Intelligence and Multi-Agent Systems

The provided document appears to be a comprehensive collection of citations and bibliographic entries rather than a coherent academic paper. These entries span numerous topics and areas within the fields of artificial intelligence, machine learning, distributed systems, decision theory, and game theory. Given the breadth of subjects covered and the absence of specific research content, a detailed analysis will focus on conceptual connections and trends across these areas, particularly those relevant to distributed artificial intelligence (DAI) and multi-agent systems (MAS).

Distributed Artificial Intelligence and Multi-Agent Systems

Distributed Artificial Intelligence is an area focused on problem-solving that involves multiple autonomous agents, each with some degree of independence, autonomy, and capability to interact with other agents within a system. The entries related to DAI and MAS suggest sustained interest in addressing how autonomous agents synchronize their activities to achieve complex goals. One of the foundational concepts referenced, particularly through works like those of Victor Lesser and colleagues, includes cooperative problem-solving and negotiation among agents, which is pivotal in designing systems where agents must work together to allocate resources efficiently or resolve conflicts.

Coordination and Negotiation among Agents

Sections of the referential data highlight issues related to negotiation strategies and multi-agent coordination, such as those discussed by Rosenschein and Zlotkin. Negotiation in MAS often involves reaching agreements that are beneficial to all parties, often within time constraints and under conditions of limited shared information. The literature suggests methods for resolving disagreements or conflicts through structured negotiation protocols, enhancing both global system efficiency and fairness in shared tasks.

The complexity of these tasks necessitates the development of sophisticated algorithms that can facilitate task and resource allocation in a manner that maximizes overall system utility. The Contract Net Protocol, notably discussed by Davis and Smith in multiple entries, remains a prominent framework for enabling agent coordination through announcements and bids, allowing for decentralized decision-making among cooperative independent agents.

Dynamic and Real-Time Decision Making

Another aspect gleaned from the bibliographic details concerns dynamic decision-making in real-time environments. Research conducted by Thomas Dean and Michael Boddy on time-dependent planning underscores the challenges agents face in environments where decisions must be made swiftly and potentially under uncertainty. Tools like anytime algorithms, capable of producing improving approximations over time, are crucial in prevailing computing scenarios where time-to-decision is as vital as the decision quality itself.

Applications in Economic and Game Theoretical Models

Looking at the concurrency of economic models and MAS, we find applications such as auction mechanisms, market-based task allocation, and cooperative gaming strategies to be prominent. These methods foster competitiveness and adaptive behavior among agents, leveraging market dynamics and game theoretic principles to predict and influence agent behavior in distributed environments. The auction models focus on resource distribution, achieving efficiency under competitive and cooperative settings, as referenced through works by Kurose, Simha, and financial market simulations.

Future Directions and Speculation

The landscape of distributed AI and MAS is one poised for considerable evolution, driven by advances in computational capabilities and theoretical frameworks. Progress in areas like machine learning, coupled with improved algorithmic strategies for constraint satisfaction and belief revision, will likely propel the development of more autonomous, intelligent, and adaptable multi-agent systems. Future research might focus on hybrid models that blend economic theories with explorative AI to optimize agent-based interactions in diverse and dynamic settings.

Additionally, the integration of deep learning within agent systems is anticipated to refine how agents perceive and react to their environments, potentially expanding the scope of distributed AI applications from automated logistics and network optimization to complex social and strategic simulations in game theory and economics.

While this analysis is derived from recognizing patterns in a comprehensive list of citations, subsequent exploration could more specifically address the nuanced contributions of individual entries, yielding more precise insights into evolving trends and innovations within distributed AI and multi-agent systems.