arXiv subjects

Andreas Kontogiannis

Publications and source records attributed to Andreas Kontogiannis.

11 recordsLinked to original sources

arXiv2026

The Complexity of Computing Nash Equilibria in Colonel Blotto Games

We study the complexity of Nash equilibrium computation in discrete Colonel Blotto games. For two-player general-sum Colonel Blotto with monotonic piecewise-constant battlefield payoffs, we show that computing an inverse-polynomial approximate Nash equilibrium is PPAD-hard, even with only two battlefields and a constant number of pieces per battlefield, thereby resolving an open question of [KPF+25]. Allowing more battlefields, the hardness persists when every battlefield payoff is $2$-piecewise constant with respect to either player's allocation. A general PPAD-membership theorem for multiplayer Blotto with arbitrary local reward functions then implies PPAD-completeness for both hardness results. Motivated by fixed-rank bimatrix games, we then identify a tractable frontier within two-player general-sum Colonel Blotto. If the social payoff has rank-$r$ structure, then, for every fixed $r$, an $\varepsilon$-Nash equilibrium can be computed in time polynomial in $B_1,B_2,k$, and $1/\varepsilon$. Thus constant-rank two-player Colonel Blotto remains tractable despite its exponentially large pure strategy spaces. Finally, we study multiplayer winner-takes-all Colonel Blotto with player-specific battlefield values and uncover a sharp tie-breaking frontier. If every highest bidder receives her full battlefield value, an exact pure Nash equilibrium can be computed in polynomial time for arbitrary binary-encoded budgets. In contrast, under ordinary equal splitting among highest bidders, we prove that computing an inverse-polynomial-accuracy Nash equilibrium is PPAD-hard even with only five players. This resolves an open question posed in concurrent work by Bichler and Ghosh [BG26], who established PPAD-hardness in the same player-specific equal-splitting setting when the number of players grows with the instance and asked whether hardness persists for a constant number of players.

cs.GT↗

arXiv2026

Finding a Positive Index Nash Equilibrium is PPADS-Complete

Every nondegenerate bimatrix game has a Nash equilibrium of Shapley index +1, since all equilibria are isolated, have index +1 or -1, and their indices sum to +1. We prove that the following promise search problem is PPADS-complete: given a rational bimatrix game promised to be nondegenerate, find an exact Nash equilibrium of index +1. The nondegeneracy promise can be removed if nonregular equilibria are also accepted: finding either a regular Nash equilibrium of index +1 or a nonregular Nash equilibrium in an arbitrary rational bimatrix game is also PPADS-complete. To our knowledge, this is the first PPADS-complete equilibrium search problem whose instances are explicit rational normal form payoff matrices, rather than succinct circuits or Turing machines, and thereby addresses an open question posed by Daskalakis [Daskalakis, 2019].

cs.CC↗

arXiv2026

The Complexity of Computing Coarse Correlated Equilibria in Markov Games with a Single Controller

We study the complexity of computing stationary Markov coarse correlated equilibria (CCE) in discounted single-controller stochastic (Markov) games [PR81, FV97], a fundamental subclass of stochastic games in which all players may affect rewards, but only one player controls the state transitions. Prior work [DGZ23, JMS23, HN25] established PPAD-hardness for computing stationary Markov CCE in two-player general-sum stochastic games via turn-based constructions in which each state is controlled by a single player, with control alternating across states. This structure forces every Markov CCE to collapse to a Nash equilibrium (NE), so hardness for NE transfers immediately to CCE. It remained open whether hardness persists when a single player controls all transitions--a setting where no such collapse occurs. We resolve this question: computing an approximate stationary Markov CCE in two-player single-controller stochastic games is PPAD-complete, even with a fixed discount factor and binary actions. For the perfect notion (equilibrium constraints at every state) this holds unconditionally at constant accuracy; for the non-perfect notion, we prove constant-accuracy hardness under the PCP-for-PPAD hypothesis [BPR16, DFHM26] and inverse-polynomial-accuracy hardness unconditionally. To the best of our knowledge, our result is the first to show hardness for computing CCE without relying on equilibrium collapse phenomena or other routes through Nash-like structure [FGK23, AKSZ24, PR24]. Instead, we construct single-controller gadgets whose local incentive constraints force a solution of a Pure-Circuit instance even under strongly correlated stationary policies.

cs.GT↗

arXiv2026

Online Learning on Hidden-Convex Losses via Algorithmic Equivalence: Optimal Regret, Geometric Barrier, and Bandit Feedback

We study adversarial online learning with hidden-convex losses, i.e., nonconvex losses that become convex after a nonlinear reparameterization. Ghai, Lu and Hazan (2022) proved that, under geometric and smoothness assumptions, online gradient descent (OGD) on such nonconvex losses approximately simulates online mirror descent (OMD) on the underlying convex losses with a suitable regularizer, yielding $\mathcal{O}(T^{2/3})$ regret. They left open whether the optimal $Θ(\sqrt{T})$ regret from online convex optimization can be recovered in this hidden-convex setting. We answer this question affirmatively. More specifically, via a sharper discrete-time algorithmic equivalence argument, we prove that OGD achieves $\mathcal{O}(\sqrt{T})$ regret under the same assumptions, matching the optimal worst-case rate for adversarial online convex optimization. We also address another open question of Ghai, Lu and Hazan (2022) by clarifying the geometry required for this algorithmic equivalence. We replace the diagonal-Jacobian sufficient condition with a necessary-and-sufficient Hessian compatibility condition, thereby expanding the class of admissible reparameterizations. We complement our tight regret bound with a lower bound showing that the Hessian compatibility assumption is essential for OGD; when it fails, we construct a smooth reparameterization and an adversarial sequence of hidden-convex losses for which OGD suffers $Ω(T)$ regret. Finally, we extend our analysis to one-point bandit feedback and prove a $\mathcal{O}(T^{3/4})$ expected regret bound for bandit OGD with spherical smoothing, matching its classical rate on convex losses.

cs.LG↗

arXiv2026

The Computational Complexity of Avoiding Strict Saddle Points in Constrained Optimization

While first-order stationary points (FOSPs) are the traditional targets of non-convex optimization, they often correspond to undesirable strict saddle points. To circumvent this, attention has shifted towards second-order stationary points (SOSPs). In unconstrained settings, finding approximate SOSPs is PLS-complete (Kontogiannis et al.), matching the complexity of finding unconstrained FOSPs (Hollender and Zampetakis). However, the complexity of finding SOSPs in constrained settings remained notoriously unclear and was highlighted as an important open question by both aforementioned works. Under one strict definition, even verifying whether a point is an approximate SOSP is NP-hard (Murty and Kabadi). Under another widely adopted, relaxed definition where non-negative curvature is required only along the null space of the active constraints, the problem lies in TFNP, and algorithms with O(poly(1/epsilon)) running times have been proposed (Lu et al.). In this work, we settle the complexity of constrained SOSP by proving that computing an epsilon-approximate SOSP under the tractable definition is PLS-complete. We demonstrate that our result holds even in the 2D unit square [0,1]^2, and remarkably, even when stationary points are isolated at a distance of Omega(1) from the domain's boundary. Our result establishes a fundamental barrier: unless PLS is a subset of PPAD (implying PLS = CLS), no deterministic, iterative algorithm with an efficient, continuous update rule can exist for finding approximate SOSPs. This contrasts with the constrained first-order counterpart, for which Fearnley et al. showed that finding an approximate KKT point is CLS-complete. Finally, our result yields the first problem defined in a compact domain to be shown PLS-complete beyond the canonical Real-LocalOpt (Daskalakis and Papadimitriou)."

cs.CC↗

arXiv2026

Efficient Swap Regret Minimization in Combinatorial Bandits

This paper addresses the problem of designing efficient no-swap regret algorithms for combinatorial bandits, where the number of actions $N$ is exponentially large in the dimensionality of the problem. In this setting, designing efficient no-swap regret translates to sublinear -- in horizon $T$ -- swap regret with polylogarithmic dependence on $N$. In contrast to the weaker notion of external regret minimization - a problem which is fairly well understood in the literature - achieving no-swap regret with a polylogarithmic dependence on $N$ has remained elusive in combinatorial bandits. Our paper resolves this challenge, by introducing a no-swap-regret learning algorithm with regret that scales polylogarithmically in $N$ and is tight for the class of combinatorial bandits. To ground our results, we also demonstrate how to implement the proposed algorithm efficiently -- that is, with a per-iteration complexity that also scales polylogarithmically in $N$ -- across a wide range of well-studied applications.

cs.LG↗

arXiv2025

Efficient Kernelized Learning in Polyhedral Games Beyond Full-Information: From Colonel Blotto to Congestion Games

We examine the problem of efficiently learning coarse correlated equilibria (CCE) in polyhedral games, that is, normal-form games with an exponentially large number of actions per player and an underlying combinatorial structure. Prominent examples of such games are the classical Colonel Blotto and congestion games. To achieve computational efficiency, the learning algorithms must exhibit regret and per-iteration complexity that scale polylogarithmically in the size of the players' action sets. This challenge has recently been addressed in the full-information setting, primarily through the use of kernelization. However, in the case of the realistic, but mathematically challenging, partial-information setting, existing approaches result in suboptimal and impractical runtime complexity to learn CCE. We tackle this limitation by building a framework based on the kernelization paradigm. We apply this framework to prominent examples of polyhedral games -- namely the Colonel Blotto, graphic matroid and network congestion games -- and provide computationally efficient payoff-based learning algorithms, which significantly improve upon prior works in terms of the runtime for learning CCE in these settings.

cs.GT↗

arXiv2025

An Extended Benchmarking of Multi-Agent Reinforcement Learning Algorithms in Complex Fully Cooperative Tasks

Multi-Agent Reinforcement Learning (MARL) has recently emerged as a significant area of research. However, MARL evaluation often lacks systematic diversity, hindering a comprehensive understanding of algorithms' capabilities. In particular, cooperative MARL algorithms are predominantly evaluated on benchmarks such as SMAC and GRF, which primarily feature team game scenarios without assessing adequately various aspects of agents' capabilities required in fully cooperative real-world tasks such as multi-robot cooperation and warehouse, resource management, search and rescue, and human-AI cooperation. Moreover, MARL algorithms are mainly evaluated on low dimensional state spaces, and thus their performance on high-dimensional (e.g., image) observations is not well-studied. To fill this gap, this paper highlights the crucial need for expanding systematic evaluation across a wider array of existing benchmarks. To this end, we conduct extensive evaluation and comparisons of well-known MARL algorithms on complex fully cooperative benchmarks, including tasks with images as agents' observations. Interestingly, our analysis shows that many algorithms, hailed as state-of-the-art on SMAC and GRF, may underperform standard MARL baselines on fully cooperative benchmarks. Finally, towards more systematic and better evaluation of cooperative MARL algorithms, we have open-sourced PyMARLzoo+, an extension of the widely used (E)PyMARL libraries, which addresses an open challenge from [TBG++21], facilitating seamless integration and support with all benchmarks of PettingZoo, as well as Overcooked, PressurePlate, Capture Target and Box Pushing.

cs.LG↗

arXiv2025

Enhancing Cooperative Multi-Agent Reinforcement Learning with State Modelling and Adversarial Exploration

Learning to cooperate in distributed partially observable environments with no communication abilities poses significant challenges for multi-agent deep reinforcement learning (MARL). This paper addresses key concerns in this domain, focusing on inferring state representations from individual agent observations and leveraging these representations to enhance agents' exploration and collaborative task execution policies. To this end, we propose a novel state modelling framework for cooperative MARL, where agents infer meaningful belief representations of the non-observable state, with respect to optimizing their own policies, while filtering redundant and less informative joint state information. Building upon this framework, we propose the MARL SMPE algorithm. In SMPE, agents enhance their own policy's discriminative abilities under partial observability, explicitly by incorporating their beliefs into the policy network, and implicitly by adopting an adversarial type of exploration policies which encourages agents to discover novel, high-value states while improving the discriminative abilities of others. Experimentally, we show that SMPE outperforms state-of-the-art MARL algorithms in complex fully cooperative tasks from the MPE, LBF, and RWARE benchmarks.

cs.LG↗

arXiv2025

Tree-based Focused Web Crawling with Reinforcement Learning

A focused crawler aims at discovering as many web pages and web sites relevant to a target topic as possible, while avoiding irrelevant ones. Reinforcement Learning (RL) has been a promising direction for optimizing focused crawling, because RL can naturally optimize the long-term profit of discovering relevant web locations within the context of a reward. In this paper, we propose TRES, a novel RL-empowered framework for focused crawling that aims at maximizing both the number of relevant web pages (aka \textit{harvest rate}) and the number of relevant web sites (\textit{domains}). We model the focused crawling problem as a novel Markov Decision Process (MDP), which the RL agent aims to solve by determining an optimal crawling strategy. To overcome the computational infeasibility of exhaustively searching for the best action at each time step, we propose Tree-Frontier, a provably efficient tree-based sampling algorithm that adaptively discretizes the large state and action spaces and evaluates only a few representative actions. Experimentally, utilizing online real-world data, we show that TRES significantly outperforms and Pareto-dominates state-of-the-art methods in terms of harvest rate and the number of retrieved relevant domains, while it provably reduces by orders of magnitude the number of URLs needed to be evaluated at each crawling step.

cs.IR↗

arXiv2023

XDQN: Inherently Interpretable DQN through Mimicking

Although deep reinforcement learning (DRL) methods have been successfully applied in challenging tasks, their application in real-world operational settings is challenged by methods' limited ability to provide explanations. Among the paradigms for explainability in DRL is the interpretable box design paradigm, where interpretable models substitute inner constituent models of the DRL method, thus making the DRL method "inherently" interpretable. In this paper we explore this paradigm and we propose XDQN, an explainable variation of DQN, which uses an interpretable policy model trained through mimicking. XDQN is challenged in a complex, real-world operational multi-agent problem, where agents are independent learners solving congestion problems. Specifically, XDQN is evaluated in three MARL scenarios, pertaining to the demand-capacity balancing problem of air traffic management. XDQN achieves performance similar to that of DQN, while its abilities to provide global models' interpretations and interpretations of local decisions are demonstrated.

cs.LG↗