Related papers: The Aldous--Lyons Conjecture II: Undecidability
We consider differentiable games where the goal is to find a Nash equilibrium. The machine learning community has recently started using variants of the gradient method (GD). Prime examples are extragradient (EG), the optimistic gradient…
We study the problem of guaranteeing low regret in repeated games against an opponent with unknown membership in one of several classes. We add the constraint that our algorithm is non-exploitable, in that the opponent lacks an incentive to…
We study hedonic coalition formation games in which cooperation among the players is restricted by a graph structure: a subset of players can form a coalition if and only if they are connected in the given graph. We investigate the…
Evaluating and optimizing policies in the presence of unobserved confounders is a problem of growing interest in offline reinforcement learning. Using conventional methods for offline RL in the presence of confounding can not only lead to…
We investigate the local linear convergence properties of the Alternating Direction Method of Multipliers (ADMM) when applied to Semidefinite Programming (SDP). A longstanding belief suggests that ADMM is only capable of solving SDPs to…
In classical complexity theory, the two definitions of probabilistically checkable proofs -- the constraint satisfaction and the nonlocal games version -- are computationally equal in power. In the quantum setting, the situation is far less…
Decision making in modern large-scale and complex systems such as communication networks, smart electricity grids, and cyber-physical systems motivate novel game-theoretic approaches. This paper investigates big strategic (non-cooperative)…
Many recent AI architectures are inspired by zero-sum games, however, the behavior of their dynamics is still not well understood. Inspired by this, we study standard gradient descent ascent (GDA) dynamics in a specific class of non-convex…
The inner alignment problem, which asserts whether an arbitrary artificial intelligence (AI) model satisfices a non-trivial alignment function of its outputs given its inputs, is undecidable. This is rigorously proved by Rice's theorem,…
We show undecidability of the satisfiability problem of what is arguably the simplest non-sub-Boolean modal logic with an implicit notion of binding. This work enriches the series of existing results of undecidability of modal logics with…
In the setting of a self-dual cone in a finite-dimensional inner product space, we consider (zero-sum) linear games. In our previous work, we showed that a Z-transformation with positive value is completely mixed. The present paper…
Generalized trust-region subproblem (GT) is a nonconvex quadratic optimization with a single quadratic constraint. It reduces to the classical trust-region subproblem (T) if the constraint set is a Euclidean ball. (GT) is polynomially…
We consider the dynamic behavior of several variants of the Network Creation Game, introduced by Fabrikant et al. [PODC'03]. Equilibrium networks in these models have desirable properties like low social cost and small diameter, which makes…
Anomaly detection is a method for discovering unusual and suspicious behavior. In many real-world scenarios, the examined events can be directly linked to the actions of an adversary, such as attacks on computer networks or frauds in…
We identify a subproblem of the model-checking problem for the epistemic \mu-calculus which is decidable. Formulas in the instances of this subproblem allow free variables within the scope of epistemic modalities in a restricted form that…
In this paper, we introduce post-selection games, a generalization of nonlocal games where each round can be not only won or lost by the players, but also discarded by the referee. Such games naturally formalize possibilistic proofs of…
Extended non-local games are a generalization of monogamy-of-entanglement games, played by two quantum parties and a quantum referee that performs a measurement on their local quantum system. Along the lines of the NPA hierarchy, the…
We study online learning in two-player uninformed Markov games, where the opponent's actions and policies are unobserved. In this setting, Tian et al. (2021) show that achieving no-external-regret is impossible without incurring an…
We use a recently discovered constrained de Finetti reduction (aka "Post-Selection Lemma") to study the parallel repetition of multi-player non-local games under no-signalling strategies. Since the technique allows us to reduce general…
Wide machine learning tasks can be formulated as non-convex multi-player games, where Nash equilibrium (NE) is an acceptable solution to all players, since no one can benefit from changing its strategy unilaterally. Attributed to the…