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Complement Submodular Information Measures for Balanced and Robust Data Selection A Proof of a Conjecture on Positive and Negative Square Energies of Unicyclic Graphs Laplacian Spectrum of the Weakly Zero-Divisor Graph of a Finite Commutative Ring An identity for second Eulerian numbers via lattice-point counting $t$-tone edge coloring of graphs Constructing Maximal Bumpless Pipedreams for Double Grothendieck Polynomials Mubayi's Polynomial-Ideal Conjecture and Cover-Ideal Turán Methods Implicit Binarization via Complex Phase Dynamics in Combinatorial Optimization The limits of Schur multipliers in Pólya conversion problems for the $q$-permanent function Universality theorems for generalized splines Framing Triangulations for Arbitrary Integer Flow Polytopes On the Common Generalization of Gentle Algebras and Framed Directed Acyclic Graphs The complexity of frugal digraph homomorphisms Chaotic and periodic behavior of jeu de taquin on infinite Young tableaux Enumerating Pattern Avoiding Parking Functions Incidence toric ideals and three-point functions Unique Winning Opening Move in Three-Row Chomp Strong majority colorings of graphs A Balancing Theorem for Spanning Trees of Rectangular Grid Graphs Spectral radius and edge-disjoint connected factors of graphs New invariants for rank metric codes, with applications to the classification of rank two semifields of order 256 Flexible DP-4-coloring of planar graphs without 4-cycles and intersecting triangles Balanced intersection size distributions in projective planes List Reconstruction Problem with List Size Two Is Dimensionality a Barrier for Retrieval Models? The INIEP: Irreducible and Positive Realizations The number of Pfaffian orientations on punctured polygonally cellulated surfaces Explicit Construction of Polytopes whose Ehrhart Polynomials Realize any Given Sign Pattern Finite-state enumeration of adjacency-constrained 132-avoiding permutations AMDS and quantum AMDS Constacyclic codes of length $4p^ς$ over $\mathbb{F}_{{p}^{m}}$
General Performance Evaluation for Competitive Resource A...
N'yoma Diamond, Fabricio Murai · 2024-01-09 · via math.CO updates on arXiv.org

Many high-stakes decision-making problems, such as those found within cybersecurity and economics, can be modeled as competitive resource allocation games. In these games, multiple players must allocate limited resources to overcome their opponent(s), while minimizing any induced individual losses. However, existing means of assessing the performance of resource allocation algorithms are highly disparate and problem-dependent. As a result, evaluating such algorithms is unreliable or impossible in many contexts and applications, especially when considering differing levels of feedback. To resolve this problem, we propose a generalized definition of payoff which uses an arbitrary user-provided function. This unifies performance evaluation under all contexts and levels of feedback. Using this definition, we develop metrics for evaluating player performance, and estimators to approximate them under uncertainty (i.e., bandit or semi-bandit feedback). These metrics and their respective estimators provide a problem-agnostic means to contextualize and evaluate algorithm performance. To validate the accuracy of our estimator, we explore the Colonel Blotto ($\mathcal{CB}$) game as an example. To this end, we propose a graph-pruning approach to efficiently identify feasible opponent decisions, which are used in computing our estimation metrics. Using various resource allocation algorithms and game parameters, a suite of $\mathcal{CB}$ games are simulated and used to compute and evaluate the quality of our estimates. These simulations empirically show our approach to be highly accurate at estimating the metrics associated with the unseen outcomes of an opponent's latent behavior.