Related papers: Ordinal Folding Index: A Computable Metric for Sel…
We develop an operator algebraic framework for infinite games with a continuum of agents and prove that regret based learning dynamics governed by a noncommutative continuity equation converge to a unique quantal response equilibrium under…
Closed-loop decision-making systems (e.g., lending, screening, or recidivism risk assessment) often operate under fairness and service constraints while inducing feedback effects: decisions change who appears in the future, yielding…
Ordinal regression predicts the objects' labels that exhibit a natural ordering, which is important to many managerial problems such as credit scoring and clinical diagnosis. In these problems, the ability to explain how the attributes…
Ordinal Classification (OC) addresses those classification tasks where the labels exhibit a natural order. Unlike nominal classification, which treats all classes as mutually exclusive and unordered, OC takes the ordinal relationship into…
The goal of ordinal embedding is to represent items as points in a low-dimensional Euclidean space given a set of constraints in the form of distance comparisons like "item $i$ is closer to item $j$ than item $k$". Ordinal constraints like…
In this paper we consider a fragment of the first-order theory of the real numbers that includes systems of equations of continuous functions in bounded domains, and for which all functions are computable in the sense that it is possible to…
Given a dynamic ordinal game, we deem a strategy sequentially rational if there exist a Bernoulli utility function and a conditional probability system with respect to which the strategy is a maximizer. We establish a complete class theorem…
Most existing results about \emph{last-iterate convergence} of learning dynamics are limited to two-player zero-sum games, and only apply under rigid assumptions about what dynamics the players follow. In this paper we provide new results…
Building AI systems that can plan, act, and create in the physical world requires more than pattern recognition. Such systems must understand the causal mechanisms and constraints governing physical processes in order to guide sequential…
We study the extent to which it is possible to approximate the optimal value of a Unique Games instance in Fixed-Point Logic with Counting (FPC). Formally, we prove lower bounds against the accuracy of FPC-interpretations that map Unique…
American football is unique in that offensive and defensive units typically consist of separate players who don't share the field simultaneously, which tempts one to evaluate them independently. However, a team's offensive and defensive…
One of the elegant achievements in the history of proof theory is the characterization of the provably total recursive functions of an arithmetical theory by its proof-theoretic ordinal as a way to measure the time complexity of the…
In order to give appropriate semantics to qualitative conditionals of the form "if A then normally B", ordinal conditional functions (OCFs) ranking the possible worlds according to their degree of plausibility can be used. An OCF accepting…
First Order Logic (FOL) is a powerful reasoning tool for program verification. Recent work on Ivy shows that FOL is well suited for verification of parameterized distributed systems. However, specifying many natural objects, such as a ring…
We develop value iteration-based algorithms to solve in a unified manner different classes of combinatorial zero-sum games with mean-payoff type rewards. These algorithms rely on an oracle, evaluating the dynamic programming operator up to…
Estimating discrete games of complete information is often computationally difficult due to partial identification and the absence of closed-form moment characterizations. This paper proposes computationally tractable approaches to…
This work is a contribution to the study of rewrite games. Positions are finite words, and the possible moves are defined by a finite number of local rewriting rules. We introduce and investigate taking-and-merging games, that is, where…
We present a new theoretical framework that unifies category-theoretic fixed-point constructions, transfinite recursion, and game-based semantics to model how interpretations of language can stabilize through unlimited self-reference. By…
Specially customised Entropies are widely applied in measuring the degree of uncertainties existing in the frame of discernment. However, all of these entropies regard the frame as a whole that has already been determined which dose not…
We investigate infinitary wellfounded systems for linear logic with fixed points, with transfinite branching rules indexed by some closure ordinal $\alpha$ for fixed points. Our main result is that provability in the system for some…