Whether or not a country is at war, or experiencing escalating or deescalating levels of conflict, has massive ramifications on a country's national and foreign policy. Given a country's history of conflict, or lack thereof, future predictions about the war-status of a country are valuable information. In this paper, we present the use of conformal prediction on temporally-dependent data to obtain prediction sets of possible future conflict state-sequences. More specifically, we compare the results of conformal prediction to a likelihood-based prediction strategy when the data are assumed to come from a discrete-state Markov process. A point-prediction may not supply sufficient information because the penalty for a wrong prediction is extreme, and so we consider a machine learning alternative that gives valid uncertainty quantification and is robust to model misspecification. In the data analysis, we present real forecasts of conflict dynamics across multiple countries. Lastly, we comment on the possible limitations of existing approaches for applying conformal prediction to Markovian data, where the exchangeability assumption is violated.

Forouranalysis wedevise several concentration results forMarkovchains, including amaximal inequality for Markov chains, that may be of interest in their own right. As a byproduct of our analysis we also establish asymptotically optimal, finite-time guarantees for the case of multiple plays, and i.i.d.

Contrastive learning has emerged as a cornerstone of unsupervised representation learning across vision, language, and graph domains, with InfoNCE as its dominant objective. Despite its empirical success, the theoretical underpinnings of InfoNCE remain limited. In this work, we introduce an explicit feature space to model augmented views of samples and a transition probability matrix to capture data augmentation dynamics. We demonstrate that InfoNCE optimizes the probability of two views sharing the same source toward a constant target defined by this matrix, naturally inducing feature clustering in the representation space. Leveraging this insight, we propose Scaled Convergence InfoNCE (SC-InfoNCE), a novel loss function that introduces a tunable convergence target to flexibly control feature similarity alignment. By scaling the target matrix, SC-InfoNCE enables flexible control over feature similarity alignment, allowing the training objective to better match the statistical properties of downstream data. Experiments on benchmark datasets, including image, graph, and text tasks, show that SC-InfoNCE consistently achieves strong and reliable performance across diverse domains.

In this paper, we provide a novel algorithm for solving planning and learning problems of Markov decision processes. The proposed algorithm follows a policy iteration-type update by using a rank-one approximation of the transition probability matrix in the policy evaluation step. This rank-one approximation is closely related to the stationary distribution of the corresponding transition probability matrix, which is approximated using the power method. We provide theoretical guarantees for the convergence of the proposed algorithm to optimal (action-)value function with the same rate and computational complexity as the value iteration algorithm in the planning problem and as the Q-learning algorithm in the learning problem. Through our extensive numerical simulations, however, we show that the proposed algorithm consistently outperforms first-order algorithms and their accelerated versions for both planning and learning problems.

In restless multi-arm bandits, a central agent is tasked with optimally distributing limited resources across several bandits (arms), with each arm being a Markov decision process. In this work, we generalize the traditional restless multi-arm bandit problem with a risk-neutral objective by incorporating risk-awareness. We establish indexability conditions for the case of a risk-aware objective and provide a solution based on Whittle index. In addition, we address the learning problem when the true transition probabilities are unknown by proposing a Thompson sampling approach and show that it achieves bounded regret that scales sublinearly with the number of episodes and quadratically with the number of arms. The efficacy of our method in reducing risk exposure in restless multi-arm bandits is illustrated through a set of numerical experiments.