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Researcher profile

Gabriele Farina

Gabriele Farina contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Computer Science and Game TheoryMachine LearningArtificial IntelligenceMultiagent SystemsComputational Complexityecon.THmath.OC

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Published work

13 published item(s)

preprint2026arXiv

Computing Equilibrium beyond Unilateral Deviation

Most familiar equilibrium concepts, such as Nash and correlated equilibrium, guarantee only that no single player can improve their utility by deviating unilaterally. They offer no guarantees against profitable coordinated deviations by coalitions. Although the literature proposes solution concepts that provide stability against multilateral deviations (\emph{e.g.}, strong Nash and coalition-proof equilibrium), these generally fail to exist. In this paper, we study an alternative solution concept that minimizes coalitional deviation incentives, rather than requiring them to vanish, and is therefore guaranteed to exist. Specifically, we focus on minimizing the average gain of a deviating coalition, and extend the framework to weighted-average and maximum-within-coalition gains. In contrast, the minimum-gain analogue is shown to be computationally intractable. For the average-gain and maximum-gain objectives, we prove a lower bound on the complexity of computing such an equilibrium and present an algorithm that matches this bound. Finally, we use our framework to solve the \emph{Exploitability Welfare Frontier} (EWF), the maximum attainable social welfare subject to a given exploitability (the maximum gain over all unilateral deviations).

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

GAE Falls Short in Imperfect-Information Self-Play Reinforcement Learning

Competitive multi-agent reinforcement learning in imperfect-information games requires agents to act under partial observability and against adversarial opponents, necessitating stochastic policies. While self-play reinforcement learning with Proximal Policy Optimization (PPO) has achieved strong empirical success, its standard advantage estimator, generalized advantage estimation, suffers from additional variance due to the sampling of stochastic future actions. This variance is amplified in equilibrium self-play because of the stochastic nature of the equilibrium policy and persists even when the critic is exact. We address this bottleneck by introducing $Q$-boosting, a variance-reduced advantage estimator based on a centralized action-value critic, and propose Variance-Reduced Policy Optimization (VRPO), incorporating this new estimator. The algorithm replaces sampled multi-step backups with a multi-step Expected SARSA$(λ)$ trace, computing policy expectations at each step to average out action-sampling noise, while retaining PPO's clipped objective and on-policy actor updates. Empirically, VRPO consistently achieves strong performance from mid-sized to large-scale games including Dou Dizhu and Heads-Up No-Limit Texas Hold'em.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Clairvoyant Regret Minimization: Equivalence with Nemirovski's Conceptual Prox Method and Extension to General Convex Games

A recent paper by Piliouras et al. [2021, 2022] introduces an uncoupled learning algorithm for normal-form games -- called Clairvoyant MWU (CMWU). In this note we show that CMWU is equivalent to the conceptual prox method described by Nemirovski [2004]. This connection immediately shows that it is possible to extend the CMWU algorithm to any convex game, a question left open by Piliouras et al. We call the resulting algorithm -- again equivalent to the conceptual prox method -- Clairvoyant OMD. At the same time, we show that our analysis yields an improved regret bound compared to the original bound by Piliouras et al., in that the regret of CMWU scales only with the square root of the number of players, rather than the number of players themselves.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Faster No-Regret Learning Dynamics for Extensive-Form Correlated and Coarse Correlated Equilibria

A recent emerging trend in the literature on learning in games has been concerned with providing faster learning dynamics for correlated and coarse correlated equilibria in normal-form games. Much less is known about the significantly more challenging setting of extensive-form games, which can capture both sequential and simultaneous moves, as well as imperfect information. In this paper we establish faster no-regret learning dynamics for \textit{extensive-form correlated equilibria (EFCE)} in multiplayer general-sum imperfect-information extensive-form games. When all players follow our accelerated dynamics, the correlated distribution of play is an $O(T^{-3/4})$-approximate EFCE, where the $O(\cdot)$ notation suppresses parameters polynomial in the description of the game. This significantly improves over the best prior rate of $O(T^{-1/2})$. To achieve this, we develop a framework for performing accelerated \emph{Phi-regret minimization} via predictions. One of our key technical contributions -- that enables us to employ our generic template -- is to characterize the stability of fixed points associated with \emph{trigger deviation functions} through a refined perturbation analysis of a structured Markov chain. Furthermore, for the simpler solution concept of extensive-form \emph{coarse} correlated equilibrium (EFCCE) we give a new succinct closed-form characterization of the associated fixed points, bypassing the expensive computation of stationary distributions required for EFCE. Our results place EFCCE closer to \emph{normal-form coarse correlated equilibria} in terms of the per-iteration complexity, although the former prescribes a much more compelling notion of correlation. Finally, experiments conducted on standard benchmarks corroborate our theoretical findings.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Kernelized Multiplicative Weights for 0/1-Polyhedral Games: Bridging the Gap Between Learning in Extensive-Form and Normal-Form Games

While extensive-form games (EFGs) can be converted into normal-form games (NFGs), doing so comes at the cost of an exponential blowup of the strategy space. So, progress on NFGs and EFGs has historically followed separate tracks, with the EFG community often having to catch up with advances (e.g., last-iterate convergence and predictive regret bounds) from the larger NFG community. In this paper we show that the Optimistic Multiplicative Weights Update (OMWU) algorithm -- the premier learning algorithm for NFGs -- can be simulated on the normal-form equivalent of an EFG in linear time per iteration in the game tree size using a kernel trick. The resulting algorithm, Kernelized OMWU (KOMWU), applies more broadly to all convex games whose strategy space is a polytope with 0/1 integral vertices, as long as the kernel can be evaluated efficiently. In the particular case of EFGs, KOMWU closes several standing gaps between NFG and EFG learning, by enabling direct, black-box transfer to EFGs of desirable properties of learning dynamics that were so far known to be achievable only in NFGs. Specifically, KOMWU gives the first algorithm that guarantees at the same time last-iterate convergence, lower dependence on the size of the game tree than all prior algorithms, and $\tilde{\mathcal{O}}(1)$ regret when followed by all players.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Modeling Strong and Human-Like Gameplay with KL-Regularized Search

We consider the task of building strong but human-like policies in multi-agent decision-making problems, given examples of human behavior. Imitation learning is effective at predicting human actions but may not match the strength of expert humans, while self-play learning and search techniques (e.g. AlphaZero) lead to strong performance but may produce policies that are difficult for humans to understand and coordinate with. We show in chess and Go that regularizing search based on the KL divergence from an imitation-learned policy results in higher human prediction accuracy and stronger performance than imitation learning alone. We then introduce a novel regret minimization algorithm that is regularized based on the KL divergence from an imitation-learned policy, and show that using this algorithm for search in no-press Diplomacy yields a policy that matches the human prediction accuracy of imitation learning while being substantially stronger.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

No-Regret Learning Dynamics for Extensive-Form Correlated Equilibrium

The existence of simple, uncoupled no-regret dynamics that converge to correlated equilibria in normal-form games is a celebrated result in the theory of multi-agent systems. Specifically, it has been known for more than 20 years that when all players seek to minimize their internal regret in a repeated normal-form game, the empirical frequency of play converges to a normal-form correlated equilibrium. Extensive-form (that is, tree-form) games generalize normal-form games by modeling both sequential and simultaneous moves, as well as private information. Because of the sequential nature and presence of partial information in the game, extensive-form correlation has significantly different properties than the normal-form counterpart, many of which are still open research directions. Extensive-form correlated equilibrium (EFCE) has been proposed as the natural extensive-form counterpart to normal-form correlated equilibrium. However, it was currently unknown whether EFCE emerges as the result of uncoupled agent dynamics. In this paper, we give the first uncoupled no-regret dynamics that converge to the set of EFCEs in $n$-player general-sum extensive-form games with perfect recall. First, we introduce a notion of trigger regret in extensive-form games, which extends that of internal regret in normal-form games. When each player has low trigger regret, the empirical frequency of play is close to an EFCE. Then, we give an efficient no-trigger-regret algorithm. Our algorithm decomposes trigger regret into local subproblems at each decision point for the player, and constructs a global strategy of the player from the local solutions at each decision point.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Bandit Linear Optimization for Sequential Decision Making and Extensive-Form Games

Tree-form sequential decision making (TFSDM) extends classical one-shot decision making by modeling tree-form interactions between an agent and a potentially adversarial environment. It captures the online decision-making problems that each player faces in an extensive-form game, as well as Markov decision processes and partially-observable Markov decision processes where the agent conditions on observed history. Over the past decade, there has been considerable effort into designing online optimization methods for TFSDM. Virtually all of that work has been in the full-feedback setting, where the agent has access to counterfactuals, that is, information on what would have happened had the agent chosen a different action at any decision node. Little is known about the bandit setting, where that assumption is reversed (no counterfactual information is available), despite this latter setting being well understood for almost 20 years in one-shot decision making. In this paper, we give the first algorithm for the bandit linear optimization problem for TFSDM that offers both (i) linear-time iterations (in the size of the decision tree) and (ii) $O(\sqrt{T})$ cumulative regret in expectation compared to any fixed strategy, at all times $T$. This is made possible by new results that we derive, which may have independent uses as well: 1) geometry of the dilated entropy regularizer, 2) autocorrelation matrix of the natural sampling scheme for sequence-form strategies, 3) construction of an unbiased estimator for linear losses for sequence-form strategies, and 4) a refined regret analysis for mirror descent when using the dilated entropy regularizer.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Faster Game Solving via Predictive Blackwell Approachability: Connecting Regret Matching and Mirror Descent

Blackwell approachability is a framework for reasoning about repeated games with vector-valued payoffs. We introduce predictive Blackwell approachability, where an estimate of the next payoff vector is given, and the decision maker tries to achieve better performance based on the accuracy of that estimator. In order to derive algorithms that achieve predictive Blackwell approachability, we start by showing a powerful connection between four well-known algorithms. Follow-the-regularized-leader (FTRL) and online mirror descent (OMD) are the most prevalent regret minimizers in online convex optimization. In spite of this prevalence, the regret matching (RM) and regret matching+ (RM+) algorithms have been preferred in the practice of solving large-scale games (as the local regret minimizers within the counterfactual regret minimization framework). We show that RM and RM+ are the algorithms that result from running FTRL and OMD, respectively, to select the halfspace to force at all times in the underlying Blackwell approachability game. By applying the predictive variants of FTRL or OMD to this connection, we obtain predictive Blackwell approachability algorithms, as well as predictive variants of RM and RM+. In experiments across 18 common zero-sum extensive-form benchmark games, we show that predictive RM+ coupled with counterfactual regret minimization converges vastly faster than the fastest prior algorithms (CFR+, DCFR, LCFR) across all games but two of the poker games, sometimes by two or more orders of magnitude.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Model-Free Online Learning in Unknown Sequential Decision Making Problems and Games

Regret minimization has proved to be a versatile tool for tree-form sequential decision making and extensive-form games. In large two-player zero-sum imperfect-information games, modern extensions of counterfactual regret minimization (CFR) are currently the practical state of the art for computing a Nash equilibrium. Most regret-minimization algorithms for tree-form sequential decision making, including CFR, require (i) an exact model of the player's decision nodes, observation nodes, and how they are linked, and (ii) full knowledge, at all times t, about the payoffs -- even in parts of the decision space that are not encountered at time t. Recently, there has been growing interest towards relaxing some of those restrictions and making regret minimization applicable to settings for which reinforcement learning methods have traditionally been used -- for example, those in which only black-box access to the environment is available. We give the first, to our knowledge, regret-minimization algorithm that guarantees sublinear regret with high probability even when requirement (i) -- and thus also (ii) -- is dropped. We formalize an online learning setting in which the strategy space is not known to the agent and gets revealed incrementally whenever the agent encounters new decision points. We give an efficient algorithm that achieves $O(T^{3/4})$ regret with high probability for that setting, even when the agent faces an adversarial environment. Our experiments show it significantly outperforms the prior algorithms for the problem, which do not have such guarantees. It can be used in any application for which regret minimization is useful: approximating Nash equilibrium or quantal response equilibrium, approximating coarse correlated equilibrium in multi-player games, learning a best response, learning safe opponent exploitation, and online play against an unknown opponent/environment.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Faster Algorithms for Optimal Ex-Ante Coordinated Collusive Strategies in Extensive-Form Zero-Sum Games

We focus on the problem of finding an optimal strategy for a team of two players that faces an opponent in an imperfect-information zero-sum extensive-form game. Team members are not allowed to communicate during play but can coordinate before the game. In that setting, it is known that the best the team can do is sample a profile of potentially randomized strategies (one per player) from a joint (a.k.a. correlated) probability distribution at the beginning of the game. In this paper, we first provide new modeling results about computing such an optimal distribution by drawing a connection to a different literature on extensive-form correlation. Second, we provide an algorithm that computes such an optimal distribution by only using profiles where only one of the team members gets to randomize in each profile. We can also cap the number of such profiles we allow in the solution. This begets an anytime algorithm by increasing the cap. We find that often a handful of well-chosen such profiles suffices to reach optimal utility for the team. This enables team members to reach coordination through a relatively simple and understandable plan. Finally, inspired by this observation and leveraging theoretical concepts that we introduce, we develop an efficient column-generation algorithm for finding an optimal distribution for the team. We evaluate it on a suite of common benchmark games. It is three orders of magnitude faster than the prior state of the art on games that the latter can solve and it can also solve several games that were previously unsolvable.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Polynomial-Time Computation of Optimal Correlated Equilibria in Two-Player Extensive-Form Games with Public Chance Moves and Beyond

Unlike normal-form games, where correlated equilibria have been studied for more than 45 years, extensive-form correlation is still generally not well understood. Part of the reason for this gap is that the sequential nature of extensive-form games allows for a richness of behaviors and incentives that are not possible in normal-form settings. This richness translates to a significantly different complexity landscape surrounding extensive-form correlated equilibria. As of today, it is known that finding an optimal extensive-form correlated equilibrium (EFCE), extensive-form coarse correlated equilibrium (EFCCE), or normal-form coarse correlated equilibrium (NFCCE) in a two-player extensive-form game is computationally tractable when the game does not include chance moves, and intractable when the game involves chance moves. In this paper we significantly refine this complexity threshold by showing that, in two-player games, an optimal correlated equilibrium can be computed in polynomial time, provided that a certain condition is satisfied. We show that the condition holds, for example, when all chance moves are public, that is, both players observe all chance moves. This implies that an optimal EFCE, EFCCE and NFCCE can be computed in polynomial time in the game size in two-player games with public chance moves, providing the biggest positive complexity result surrounding extensive-form correlation in more than a decade.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Stochastic Regret Minimization in Extensive-Form Games

Monte-Carlo counterfactual regret minimization (MCCFR) is the state-of-the-art algorithm for solving sequential games that are too large for full tree traversals. It works by using gradient estimates that can be computed via sampling. However, stochastic methods for sequential games have not been investigated extensively beyond MCCFR. In this paper we develop a new framework for developing stochastic regret minimization methods. This framework allows us to use any regret-minimization algorithm, coupled with any gradient estimator. The MCCFR algorithm can be analyzed as a special case of our framework, and this analysis leads to significantly-stronger theoretical on convergence, while simultaneously yielding a simplified proof. Our framework allows us to instantiate several new stochastic methods for solving sequential games. We show extensive experiments on three games, where some variants of our methods outperform MCCFR.

0 citations0 reviewsNo code linkedOpen access