We present new results for online contention resolution schemes for the matching polytope of graphs, in the random-order (RCRS) and adversarial (OCRS) arrival models. Our results include improved selectability guarantees (i.e., lower bounds), as well as new impossibility results (i.e., upper bounds). By well-known reductions to the prophet (secretary) matching problem, a c-selectable OCRS (RCRS) implies a c-competitive algorithm for adversarial (random order) edge arrivals. Similar reductions are also known for the query-commit matching problem. For the adversarial arrival model, we present a new analysis of the OCRS of Ezra et al. (EC, 2020). We show that this scheme is 0.344-selectable for general graphs and 0.349-selectable for bipartite graphs, improving on the previous 0.337 selectability result for this algorithm. We also show that the selectability of this scheme cannot be greater than 0.361 for general graphs and 0.382 for bipartite graphs. We further show that no OCRS can achieve a selectability greater than 0.4 for general graphs, and 0.433 for bipartite graphs. For random-order arrivals, we present two attenuation-based schemes which use new attenuation functions. Our first RCRS is 0.474-selectable for general graphs, and our second is 0.476-selectable for bipartite graphs. These results improve upon the recent 0.45 (and 0.456) selectability results for general graphs (respectively, bipartite graphs) due to Pollner et al. (EC, 2022). On general graphs, our 0.474-selectable RCRS provides the best known positive result even for offline contention resolution, and also for the correlation gap. We conclude by proving a fundamental upper bound of 0.5 on the selectability of RCRS, using bipartite graphs. * The full version of the paper can be accessed at https://arxiv.org/abs/2209.07520

The main focus of this paper is radius-based (supplier) clustering in the two-stage stochastic setting with recourse, where the inherent stochasticity of the model comes in the form of a budget constraint. We also explore a number of variants where additional constraints are imposed on the first-stage decisions, specifically matroid and multi-knapsack constraints. Our eventual goal is to provide results for supplier problems in the most general distributional setting, where there is only black-box access to the underlying distribution. To that end, we follow a two-step approach. First, we develop algorithms for a restricted version of each problem, in which all possible scenarios are explicitly provided; second, we employ a novel scenario-discarding variant of the standard Sample Average Approximation (SAA) method, in which we crucially exploit properties of the restricted-case algorithms. We finally note that the scenario-discarding modification to the SAA method is necessary in order to optimize over the radius.

Matching is one of the most fundamental and broadly applicable problems across many domains. In these diverse real-world applications, there is often a degree of uncertainty in the input which has led to the study of stochastic matching models. Here, each edge in the graph has a known, independent probability of existing derived from some prediction. Algorithms must probe edges to determine existence and match them irrevocably if they exist. Further, each vertex may have a patience constraint denoting how many of its neighboring edges can be probed. We present new ordered contention resolution schemes yielding improved approximation guarantees for some of the foundational problems studied in this area. For stochastic matching with patience constraints in general graphs, we provide a $0.382$-approximate algorithm, significantly improving over the previous best $0.31$-approximation of Baveja et al. (2018). When the vertices do not have patience constraints, we describe a $0.432$-approximate random order probing algorithm with several corollaries such as an improved guarantee for the Prophet Secretary problem under Edge Arrivals. Finally, for the special case of bipartite graphs with unit patience constraints on one of the partitions, we show a $0.632$-approximate algorithm that improves on the recent $1/3$-guarantee of Hikima et al. (2021).

This paper introduces the PettingZoo library and the accompanying Agent Environment Cycle ("AEC") games model. PettingZoo is a library of diverse sets of multi-agent environments with a universal, elegant Python API. PettingZoo was developed with the goal of accelerating research in Multi-Agent Reinforcement Learning ("MARL"), by making work more interchangeable, accessible and reproducible akin to what OpenAI's Gym library did for single-agent reinforcement learning. PettingZoo's API, while inheriting many features of Gym, is unique amongst MARL APIs in that it's based around the novel AEC games model. We argue, in part through case studies on major problems in popular MARL environments, that the popular game models are poor conceptual models of the games commonly used with MARL, that they promote severe bugs that are hard to detect, and that the AEC games model addresses these problems.

Consider the following Stochastic Score Classification Problem. A doctor is assessing a patient's risk of developing a certain disease, and can perform n tests on the patient. Each test has a binary outcome, positive or negative. A positive result is an indication of risk, and a patient's score is the total number of positive test results. Test results are accurate. The doctor needs to classify the patient into one of B risk classes, depending on the score (e.g., LOW, MEDIUM, and HIGH risk). Each of these classes corresponds to a contiguous range of scores. Test i has probability p_i of being positive, and it costs c_i to perform. To reduce costs, instead of performing all tests, the doctor will perform them sequentially and stop testing when it is possible to determine the patient's risk category. The problem is to determine the order in which the doctor should perform the tests, so as to minimize expected testing cost. We provide approximation algorithms for adaptive and non-adaptive versions of this problem, and pose a number of open questions.