arXiv subjects

Darleen Perez-Lavin

Publications and source records attributed to Darleen Perez-Lavin.

3 recordsLinked to original sources

arXiv2026

Learning Strategic Value and Cooperation in Multi-Player Stochastic Games through Side Payments

We study general-sum, multi-player stochastic games with transferable utility, motivated by settings where agents can use side payments to make cooperation individually rational. Building on the Harsanyi--Shapley (HS) value for normal-form games, we introduce two HS-based value notions for stochastic games: HS-S, defined by aggregating dynamic coalition-versus-complement threat powers, and Coco-S, defined as fixed points of a statewise HS Bellman operator. We extend HS-style axioms to the stochastic setting and show that HS-S is the unique mapping satisfying them. We prove that HS-S and Coco-S coincide in all two-player stochastic games, but can disagree when $n>2$, via an explicit three-player counterexample. We prove existence and uniqueness of Coco-S fixed points for all two-player games and for three-player two-state games via topological degree theory, and provide an axiomatic characterization of Coco-S through a new \emph{Markov Consistency} axiom that distinguishes it from HS-S. Finally, we give sampling-based estimators with finite-sample guarantees and empirically compare the induced values, policies, and side payments on multi-player grid-game benchmarks.

cs.GT↗

arXiv2024

Bi-objective trail-planning for a robot team orienteering in a hazardous environment

Teams of mobile [aerial, ground, or aquatic] robots have applications in resource delivery, patrolling, information-gathering, agriculture, forest fire fighting, chemical plume source localization and mapping, and search-and-rescue. Robot teams traversing hazardous environments -- with e.g. rough terrain or seas, strong winds, or adversaries capable of attacking or capturing robots -- should plan and coordinate their trails in consideration of risks of disablement, destruction, or capture. Specifically, the robots should take the safest trails, coordinate their trails to cooperatively achieve the team-level objective with robustness to robot failures, and balance the reward from visiting locations against risks of robot losses. Herein, we consider bi-objective trail-planning for a mobile team of robots orienteering in a hazardous environment. The hazardous environment is abstracted as a directed graph whose arcs, when traversed by a robot, present known probabilities of survival. Each node of the graph offers a reward to the team if visited by a robot (which e.g. delivers a good to or images the node). We wish to search for the Pareto-optimal robot-team trail plans that maximize two [conflicting] team objectives: the expected (i) team reward and (ii) number of robots that survive the mission. A human decision-maker can then select trail plans that balance, according to their values, reward and robot survival. We implement ant colony optimization, guided by heuristics, to search for the Pareto-optimal set of robot team trail plans. As a case study, we illustrate with an information-gathering mission in an art museum.

cs.RO↗

arXiv2016

Peaks Sets of Classical Coxeter Groups

We say a permutation $π=π_1π_2\cdotsπ_n$ in the symmetric group $\mathfrak{S}_n$ has a peak at index $i$ if $π_{i-1}<π_i>π_{i+1}$ and we let $P(π)=\{i \in \{1, 2, \ldots, n\} \, \vert \, \mbox{$i$ is a peak of $π$}\}$. Given a set $S$ of positive integers, we let $P (S; n)$ denote the subset of $\mathfrak{S}_n$ consisting of all permutations $π$, where $P(π) =S$. In 2013, Billey, Burdzy, and Sagan proved $|P(S;n)| = p(n)2^{n-\lvert S\rvert-1}$, where $p(n)$ is a polynomial of degree $\max(S)- 1$. In 2014, Castro-Velez et al. considered the Coxeter group of type $B_n$ as the group of signed permutations on $n$ letters and showed that $\lvert P_B(S;n)\rvert=p(n)2^{2n-|S|-1}$ where $p(n)$ is the same polynomial of degree $\max(S)-1$. In this paper we partition the sets $P(S;n) \subset \mathfrak{S}_n$ studied by Billey, Burdzy, and Sagan into subsets of $P(S;n)$ of permutations with peak set $S$ that end with an ascent to a fixed integer $k$ or a descent and provide polynomial formulas for the cardinalities of these subsets. After embedding the Coxeter groups of Lie type $C_n$ and $D_n$ into $\mathfrak{S}_{2n}$, we partition these groups into bundles of permutations $π_1π_2 \cdotsπ_n|π_{n+1}\cdots π_{2n}$ such that $π_1π_2\cdots π_n$ has the same relative order as some permutation $σ_1σ_2\cdotsσ_n \in \mathfrak{S}_n$. This allows us to count the number of permutations in types $C_n$ and $D_n$ with a given peak set $S$ by reducing the enumeration to calculations in the symmetric group and sums across the rows of Pascal's triangle.

math.GR↗