Constant Individual Regret in General Games

Uncoupled no-regret dynamics provide a decentralized route to equilibrium, but prior guarantees for individual regret retain a polylogarithmic dependence on the horizon. We remove this dependence for every finite $N$-player normal-form game under full-information feedback. We introduce \emph{ECHO-OFTRL}: optimistic follow-the-regularized-leader (OFTRL) equipped with an EMA cascade for high-order optimism (ECHO), where EMA denotes exponential moving average. The algorithm is deterministic and fully uncoupled. If $m_{\max}$ denotes the largest action-set size, then, simultaneously for every horizon $T\geq1$, it guarantees that each of the $N$ players in the game incurs regret upper bounded by $O(\textrm{poly}(N, \log m_{\max}))$. Our algorithm leverages a new form of optimism inspired by modern filter design.

What preferences can - and cannot - predict in multi-agent online learning

We examine the interplay between ordinal, preference-based solution concepts in games and the long-run behavior of game dynamics, asking in particular to what extent the combinatorial data of a game -- its preference graph -- determine the outcomes of no-regret learning dynamics -- such as follow-the-regularized-leader (FTRL). In one direction, we show that the skeleton of every dynamically stable set (i.e. the set of pure profiles it contains) must also be preferentially stable, that is, it must be closed under profitable deviations. We then ask the converse question: when do preferences determine the long-run behavior of the players' learning dynamics? We begin by showing that preferences characterize asymptotic stability in the case of subgames -- i.e. subsets of pure profiles obtained by restricting players' action sets. Beyond this case however, the equivalence between dynamic and preferential stability collapses: concretely, we construct a three-player game with a preferentially stable set whose span is dynamically unstable, showing in this way that preferences do not suffice as a criterion of dynamic stability. We then bridge this gap via the notion of resilience under aggregate deviations, an easy-to-check payoff-based condition that guarantees asymptotic stability of arbitrary spans of pure strategies.

A Knowledge-Based Multi-Agent Framework for Security Control Recommendation

Hardening IT on-premises environments can be a daunting task for teams without access to adequate cybersecurity expertise. In this regard, Decision Support Systems (DSS) with embedded expert knowledge can assist users by guiding them with security recommendations to meet their objectives. This work proposes a Security DSS that recommends security control sub-families given minimal user requirements indicating coverage of different security dimensions. It leverages a curated, unified dataset from both well-known Information Security (InfoSec) and academic sources. This DSS is defined as a non-zero-sum, simultaneous game that is grounded in a Multi-Agent Influence Diagram (MAID) model and explores the decision space over 7 security dimensions or agents, using no-regret online learning to ultimately find the security control sub-families that best fit the requirements while incurring minimal under- and over-provisioning of security resources. This work was validated in terms of performance and accuracy, among others, for varying dataset sizes. It shows exceptional satisfaction coverage results of 99% when using as little as ~65% of the SW-implementable security controls, running in 1.2-35.7 seconds; and more moderate coverage results of 73%-77% when using ~29% of the controls, resolving in 0.8-13.8 seconds.

Optimal Coarse Correlated Equilibria in Mean Field Games: Linear Programming and No-Regret Learning

We introduce optimal coarse correlated equilibria for continuous-time mean field games. A coarse correlated equilibrium is a randomized recommendation scheme from which no player can gain by ignoring the recommendation and switching to an alternative strategy. The problem is as follows: a moderator selects, among all mean-field coarse correlated equilibria, one that optimizes a prescribed performance criterion, which may differ from the representative player's objective. After formulating the problem, we develop a linear programming (LP) formulation, prove the existence of optimal LP coarse correlated equilibria, and relate the LP characterization to the original probabilistic setting. Building on this characterization, we design a no-regret primal-dual algorithm, based on an equivalent Lagrangian formulation of the external-regret constraint, for learning such equilibria. We provide explicit convergence rates for the learning algorithm, and numerical examples illustrate the method.