Abstract We study concurrent graph games where n players cooperate against an opponent to reach a set of target states. Unlike traditional settings, we study distributed randomisation: team players do not share a source of randomness, and their private random sources are hidden from the opponent and from each other. We show that memoryless strategies are sufficient for the threshold problem (deciding whether there is a strategy for the team that ensures winning with probability that exceeds a threshold), a result that not only places the problem in the Existential Theory of the Reals ( $$\exists \mathbb {R}$$ ∃ R ) but also enables the construction of value iteration algorithms. We additionally show that the threshold problem is $$\textsf{NP}$$ NP -hard. For the almost-sure reachability problem, we prove $$\textsf{NP}$$ NP -completeness. We introduce Individually Randomised Alternating-time Temporal Logic (IRATL). This logic extends the standard ATL framework to reason about probability thresholds, with semantics explicitly designed for coalitions that lack a shared source of randomness. On the practical side, we implement and evaluate a solver for the threshold and almost-sure problem based on the algorithms that we develop.

Markov decision processes (MDPs) are a fundamental model in sequential decision making. Robust MDPs (RMDPs) extend this framework by allowing uncertainty in transition probabilities and optimizing against the worst-case realization of that uncertainty. In particular, $(s, a)$-rectangular RMDPs with $L_\infty$ uncertainty sets form a fundamental and expressive model: they subsume classical MDPs and turn-based stochastic games. We consider this model with discounted payoffs. The existence of polynomial and strongly-polynomial time algorithms is a fundamental problem for these optimization models. For MDPs, linear programming yields polynomial-time algorithms for any arbitrary discount factor, and the seminal work of Ye established strongly-polynomial time for a fixed discount factor. The generalization of such results to RMDPs has remained an important open problem. In this work, we show that a robust policy iteration algorithm runs in strongly-polynomial time for $(s, a)$-rectangular $L_\infty$ RMDPs with a constant (fixed) discount factor, resolving an important algorithmic question.

Understanding the formation of opinions on multiple interconnected topics within social networks is of significant importance. It offers insights into collective behavior and decision-making processes, with applications in Graph Neural Networks. Existing models propose that individuals form opinions based on a weighted average of their peers' opinions and potentially their own beliefs. This averaging process, when viewed as a best-response game, can be seen as an individual minimizing disagreements with peers, defined by a quadratic penalty, leading to an equilibrium. Bindel, Kleinberg, and Oren (FOCS 2011) provided tight bounds on the "price of anarchy," which is defined as the maximum level of overall disagreement at equilibrium relative to a social optimum. Bhawalkar, Gollapudi, and Munagala (STOC 2013) generalized the penalty function to consider non-quadratic penalties and provided tight bounds on the price of anarchy of these functions.

Constrained Forest Problems (CFPs) as introduced by Goemans and Williamson in 1995 capture a wide range of network design problems with edge subsets as solutions, such as Minimum Spanning Tree, Steiner Forest, and Point-to-Point Connection. While individual CFPs have been studied extensively in individual computational models, a unified approach to solving general CFPs in multiple computational models has been lacking. Against this background, we present the shell-decomposition algorithm, a model-agnostic meta-algorithm that efficiently computes a $(2+ε)$-approximation to CFPs for a broad class of forest functions. To demonstrate the power and flexibility of this result, we instantiate our algorithm for 3 fundamental, NP-hard CFPs in 3 different computational models. For example, for constant $ε$, we obtain the following $(2+ε)$-approximations in the Congest model: 1. For Steiner Forest specified via input components, where each node knows the identifier of one of $k$ disjoint subsets of $V$, we achieve a deterministic $(2+ε)$-approximation in $O(\sqrt{n}+D+k)$ rounds, where $D$ is the hop diameter of the graph. 2. For Steiner Forest specified via symmetric connection requests, where connection requests are issued to pairs of nodes, we leverage randomized equality testing to reduce the running time to $O(\sqrt{n}+D)$, succeeding with high probability. 3. For Point-to-Point Connection, we provide a $(2+ε)$-approximation in $O(\sqrt{n}+D)$ rounds. 4. For Facility Placement and Connection, a relative of non-metric Facility Location, we obtain a $(2+ε)$-approximation in $O(\sqrt{n}+D)$ rounds. We further show how to replace the $\sqrt{n}+D$ term by the complexity of solving Partwise Aggregation, achieving (near-)universal optimality in any setting in which a solution to Partwise Aggregation in near-shortcut-quality time is known.

In this work, we study active covering, a variant of the active-learning problem that involves labeling (or identifying) all of the examples with a positive label. We propose a couple of algorithms, namely Density-Adjusted Non-Adaptive (DANA) learner and Density-Adjusted Adaptive (DAA) learner, that query the labels according to a distance function that is adjusted by the density function. Under mild assumptions, we prove that our algorithms discover all of the positive labels while querying only a sublinear number of examples from the support of negative labels for constant-dimensional spaces (see Theorems 5 and 6). Our experiments show that our champion algorithm DAA consistently improves over the prior work on some standard benchmark datasets, including those used by the previous work, as well as a couple of data sets on credit card fraud. For instance, when measuring performance using AUC, our algorithm is the best in 25 out of 27 experiments over 7 different datasets.