arXiv subjects

Chun Kai Ling

Publications and source records attributed to Chun Kai Ling.

At least 19 recordsLinked to original sources

arXiv2026

Security Games on Series-Parallel Attack Graphs with Adaptive Attackers

We study security games on attack graphs, where an adaptive attacker seeks to reach a target by sequentially attempting stochastic controls along the current attack frontier, while a defender allocates limited resources across controls to delay compromise. The attacker may choose among exponentially many attack routes and freely pivot between them as successes and failures are observed, yielding an exponentially large space of contingent attack policies. For any fixed defender allocation, we show that an optimal attacker policy on a two-terminal series-parallel attack graph is an index policy: at each step, the attacker selects an available control with the largest value of an extension of the classical Gittins index. The indices and the resulting attacker best response can be computed in polynomial time, without explicitly enumerating attack paths or contingent policies. To the best of our knowledge, this is the first optimal index characterization for adaptive attackers in security games on general series-parallel attack graphs. We further develop efficient algorithms for computing the attacker's exact utility and an exact defender subgradient, enabling deterministic first-order optimization of defensive resource allocations without sampling attack trajectories. Our framework strictly generalizes prior approaches restricted to parallel chains and out-trees, while exploiting the compositional structure of series-parallel graphs to support interpretable attacker policies and parallel computation across independent subgraphs. Experiments demonstrate that the resulting methods scale substantially better than naive explicit-state approaches while producing effective defensive allocations.

cs.GT↗

arXiv2026

Computing Equilibria in Games with Stochastic Action Sets

The study of learning in games typically assumes that each player always has access to all of their actions. However, in many practical scenarios, players' available actions might be restricted due to exogenous stochasticity. To model this setting, for a game $\mathcal{G}_{\mathrm{orig}}$ with action set $A_i$ for each player $i$, we introduce the corresponding Game with Stochastic Action Sets (GSAS) which is parametrized by a probability distribution over the players' set of possible action subsets $\mathcal{S}_i \subseteq 2^{A_i}\setminus\{\varnothing\}$. In a GSAS, players' strategies and Nash equilibria (NE) admit prohibitively large representations, and existing algorithms for NE computation scale poorly. Under the assumption that action availabilities are independent between players, we show that NE in two-player zero-sum (2p0s) GSAS can be approximately represented by a compact vector of size $\vert A_i\vert$, overcoming the naïve exponential-sized representation. Computationally, we introduce an algorithm that minimizes ranking regret, converging to NE with high probability in 2p0s-GSAS with rate $O(\sqrt{\vert A_i\vert\log\vert A_i\vert/T})$. Finally, using the iterates of our algorithm, we develop a stochastic approximation procedure to recover compactly represented NE.

cs.GT↗

arXiv2026

Equilibrium Computation in Extensive-Form Games with Stochastic Action Sets

Extensive-form games (EFGs) are a standard model for sequential decision-making in games. A fundamental and typically implicit assumption in EFGs is that players always have access to all of their actions at every decision point. However, in many realistic settings, certain actions might be unavailable during game-play due to exogenous stochasticity, hindering the expressivity of the standard EFG model. Given a `base' EFG, we formalize a model that allows for actions to be stochastically restricted, leading to a corresponding Extensive-Form Games with Stochastic Action Sets (EFGSAS). In EFGSAS, we derive an expansion procedure that results in an equivalent EFG, thus showing that standard strategy formalisms could require exponentially-large representations. However, under an appropriate independence assumption, we show that compact strategy representations polynomial in the size of the base EFG exist. Computationally, we introduce an algorithm called SI-CFR that minimizes sleeping internal regret, converging to Nash equilibria with high probability in two-player zero-sum EFGSAS. Finally, we utilize a stochastic approximation procedure to recover compact representations of Nash equilibria, utilizing only the iterates of SI-CFR.

cs.GT↗

arXiv2026

Communicating Chess Strategies in Natural Language

Chess engines have long achieved superhuman playing strength. However, the underlying strategy behind their move suggestions is difficult for human players, even skilled ones, to comprehend. Motivated by this, we propose the task of chess strategy verbalization, which is to describe chess strategies in natural language. We design (i) a pipeline for verbalizing strategies and (ii) an evaluation framework for objective evaluation of generated strategy descriptions. Our experiments show that natural language is a promising and interpretable medium for communicating strategic information to both human and LLM players. We glean additional interesting insights, including (a) the importance of evaluating strategies beyond the main line, (b) the limitations of pure concept-based descriptions, and (c) the limitations of relying on LLMs rather than humans for evaluation.

cs.CL↗

arXiv2026

Enhancing Decision-Making with Large Language Models through Multi-Agent Fictitious Play

Large language model (LLM)-based multi-agent systems (MAS) have demonstrated great potential in solving tasks with execution complexity, by distributing subtasks across cooperative agents. However, this divide-and-conquer paradigm falls short on decision-making tasks that are also prevalent in the real world. These tasks require simultaneous reasoning from the stances of all involved stakeholders whose decisions are mutually dependent and thus cannot be solved in isolation. We characterize this challenge as stance entanglement, a form of decision complexity distinct from execution complexity. To address it, we propose Multi-Agent Fictitious Play (MAFP), a novel MAS paradigm that represents stakeholder stances as agents and formulates decision-making as an equilibrium-seeking process. Built on the game-theoretic principle of fictitious play, MAFP iteratively updates each agent's decision by best responding to the empirical mixture of other agents' past decisions. This enables agents to expose and address one another's weaknesses, progressively improving decision quality and robustness. We evaluate MAFP on challenging decision-making tasks that test the capability of deciding strategies for competitive scenarios prior to acting. MAFP outperforms both single-round and multi-round baselines on two complementary metrics, tournament strength and robustness, demonstrating its effectiveness in addressing stance entanglement.

cs.CL↗

arXiv2026

CARL: Criticality-Aware Agentic Reinforcement Learning

Agents capable of accomplishing complex tasks through multiple interactions with the environment have emerged as a popular research direction. However, in such multi-step settings, the conventional group-level policy optimization algorithm becomes suboptimal because of its underlying assumption that each step holds equal contribution, which deviates significantly from reality. Our analysis reveals that only the action choices on a small fraction of states are critical in determining the final outcome. Building on this insight, we propose CARL, a criticality-aware reinforcement learning algorithm tailored for long-horizon agentic reasoning. CARL leverages entropy as a heuristic proxy for state criticality and achieves focused training by assigning rewards to actions taken from high-criticality states while excluding actions taken from low-criticality states from model updates, avoiding noisy credit assignment and redundant computation. Extensive experiments demonstrate that CARL achieves both stronger performance and higher efficiency across diverse evaluation settings. The source code will be publicly available.

cs.LG↗

arXiv2026

Inference-Time Attribute Distribution Alignment for Unconditional Diffusion

Inference-time controllable generation is essential for real-world applications of unconditional diffusion models. However, most existing techniques focus on individual samples, struggling in applications that require the sample population to follow specific attribute distributions (e.g., demographic balance or semantic proportions). We formalize this setting as the inference-time attribute distributional alignment problem for pretrained unconditional diffusion models. To address this, we cast inference-time attribute distributional alignment as an optimal control problem over the reverse diffusion process, viewing the process as the rollout of a dynamical system and augmenting it with additive, time-dependent perturbations as control. We solve for the perturbations using an optimal-control-based algorithm to optimize a differentiable distribution-matching objective while penalizing control effort to preserve data fidelity. Experiment results in image generation demonstrate that our proposed plug-and-play approach can better align attribute distributions to diverse and flexible test-time targets compared to baselines, without retraining or finetuning the pretrained diffusion model.

cs.LG↗

arXiv2026

Projected Coupled Diffusion for Test-Time Constrained Joint Generation

Modifications to test-time sampling have emerged as an important extension to diffusion algorithms, with the goal of biasing the generative process to achieve a given objective without having to retrain the entire diffusion model. However, generating jointly correlated samples from multiple pre-trained diffusion models while simultaneously enforcing task-specific constraints without costly retraining has remained challenging. To this end, we propose Projected Coupled Diffusion (PCD), a novel test-time framework for constrained joint generation. PCD introduces a coupled guidance term into the generative dynamics to encourage coordination between diffusion models and incorporates a projection step at each diffusion step to enforce hard constraints. Empirically, we demonstrate the effectiveness of PCD in application scenarios of image-pair generation, object manipulation, and multi-robot motion planning. Our results show improved coupling effects and guaranteed constraint satisfaction without incurring excessive computational costs.

cs.LG↗

arXiv2026

Game of Thought: Robust Information Seeking with Large Language Models Using Game Theory

Large Language Models (LLMs) are increasingly deployed in real-world scenarios where they may lack sufficient information to complete a given task. In such settings, the ability to actively seek out missing information becomes a critical capability. Existing approaches to enhancing this ability often rely on simplifying assumptions that degrade \textit{worst-case} performance. This is an issue with serious implications in high-stakes applications. In this work, we use the game of Twenty Questions to evaluate the information-seeking ability of LLMs. We introduce and formalize its adversarial counterpart, the Strategic Language Search (SLS) problem along with its variants as a two-player zero-sum extensive form game. We propose Game of Thought (GoT), a framework that applies game-theoretic techniques to approximate a Nash equilibrium (NE) strategy for the restricted variant of the game. Empirical results demonstrate that our approach consistently improves worst-case performance compared to (1) direct prompting-based methods and (2) heuristic-guided search methods across all tested settings.

cs.CL↗

arXiv2025

Colonel Blotto with Battlefield Games

We study a class of two-player zero-sum Colonel Blotto games in which, after allocating soldiers across battlefields, players engage in (possibly distinct) normal-form games on each battlefield. Per-battlefield payoffs are parameterized by the soldier allocations. This generalizes the classical Blotto setting, where outcomes depend only on relative soldier allocations. We consider both discrete and continuous allocation models and examine two types of aggregate objectives: linear aggregation and worst-case battlefield value. For each setting, we analyze the existence and computability of Nash equilibrium. The general problem is not convex-concave, which limits the applicability of standard convex optimization techniques. However, we show that in several settings it is possible to reformulate the strategy space in a way where convex-concave structure is recovered. We evaluate the proposed methods on synthetic and real-world instances inspired by security applications, suggesting that our approaches scale well in practice.

cs.GT↗

arXiv2025

DDPS: Discrete Diffusion Posterior Sampling for Paths in Layered Graphs

Diffusion models form an important class of generative models today, accounting for much of the state of the art in cutting edge AI research. While numerous extensions beyond image and video generation exist, few of such approaches address the issue of explicit constraints in the samples generated. In this paper, we study the problem of generating paths in a layered graph (a variant of a directed acyclic graph) using discrete diffusion models, while guaranteeing that our generated samples are indeed paths. Our approach utilizes a simple yet effective representation for paths which we call the padded adjacency-list matrix (PALM). In addition, we show how to effectively perform classifier guidance, which helps steer the sampled paths to specific preferred edges without any retraining of the diffusion model. Our preliminary results show that empirically, our method outperforms alternatives which do not explicitly account for path constraints.

cs.LG↗

arXiv2024

Commitment to Sparse Strategies in Two-Player Games

While Nash equilibria are guaranteed to exist, they may exhibit dense support, making them difficult to understand and execute in some applications. In this paper, we study $k$-sparse commitments in games where one player is restricted to mixed strategies with support size at most $k$. Finding $k$-sparse commitments is known to be computationally hard. We start by showing several structural properties of $k$-sparse solutions, including that the optimal support may vary dramatically as $k$ increases. These results suggest that naive greedy or double-oracle-based approaches are unlikely to yield practical algorithms. We then develop a simple approach based on mixed integer linear programs (MILPs) for zero-sum games, general-sum Stackelberg games, and various forms of structured sparsity. We also propose practical algorithms for cases where one or both players have large (i.e., practically innumerable) action sets, utilizing a combination of MILPs and incremental strategy generation. We evaluate our methods on synthetic and real-world scenarios based on security applications. In both settings, we observe that even for small support sizes, we can obtain more than $90\%$ of the true Nash value while maintaining a reasonable runtime, demonstrating the significance of our formulation and algorithms.

cs.GT↗

arXiv2024

A short note about the learning-augmented secretary problem

We consider the secretary problem through the lens of learning-augmented algorithms. As it is known that the best possible expected competitive ratio is $1/e$ in the classic setting without predictions, a natural goal is to design algorithms that are 1-consistent and $1/e$-robust. Unfortunately, [FY24] provided hardness constructions showing that such a goal is not attainable when the candidates' true values are allowed to scale with $n$. Here, we provide a simple and explicit alternative hardness construction showing that such a goal is not achievable even when the candidates' true values are constants that do not scale with $n$.

cs.DS↗

arXiv2024

Contested Logistics: A Game-Theoretic Approach

We introduce Contested Logistics Games, a variant of logistics problems that account for the presence of an adversary that can disrupt the movement of goods in selected areas. We model this as a large two-player zero-sum one-shot game played on a graph representation of the physical world, with the optimal logistics plans described by the (possibly randomized) Nash equilibria of this game. Our logistics model is fairly sophisticated, and is able to handle multiple modes of transport and goods, accounting for possible storage of goods in warehouses, as well as Leontief utilities based on demand satisfied. We prove computational hardness results related to equilibrium finding and propose a practical double-oracle solver based on solving a series of best-response mixed-integer linear programs. We experiment on both synthetic and real-world maps, demonstrating that our proposed method scales to reasonably large games. We also demonstrate the importance of explicitly modeling the capabilities of the adversary via ablation studies and comparisons with a naive logistics plan based on heuristics.

cs.GT↗

arXiv2024

Deep Copula-Based Survival Analysis for Dependent Censoring with Identifiability Guarantees

Censoring is the central problem in survival analysis where either the time-to-event (for instance, death), or the time-tocensoring (such as loss of follow-up) is observed for each sample. The majority of existing machine learning-based survival analysis methods assume that survival is conditionally independent of censoring given a set of covariates; an assumption that cannot be verified since only marginal distributions is available from the data. The existence of dependent censoring, along with the inherent bias in current estimators has been demonstrated in a variety of applications, accentuating the need for a more nuanced approach. However, existing methods that adjust for dependent censoring require practitioners to specify the ground truth copula. This requirement poses a significant challenge for practical applications, as model misspecification can lead to substantial bias. In this work, we propose a flexible deep learning-based survival analysis method that simultaneously accommodate for dependent censoring and eliminates the requirement for specifying the ground truth copula. We theoretically prove the identifiability of our model under a broad family of copulas and survival distributions. Experiments results from a wide range of datasets demonstrate that our approach successfully discerns the underlying dependency structure and significantly reduces survival estimation bias when compared to existing methods.

stat.ML↗

arXiv2024

Multimodal Learning Without Labeled Multimodal Data: Guarantees and Applications

In many machine learning systems that jointly learn from multiple modalities, a core research question is to understand the nature of multimodal interactions: how modalities combine to provide new task-relevant information that was not present in either alone. We study this challenge of interaction quantification in a semi-supervised setting with only labeled unimodal data and naturally co-occurring multimodal data (e.g., unlabeled images and captions, video and corresponding audio) but when labeling them is time-consuming. Using a precise information-theoretic definition of interactions, our key contribution is the derivation of lower and upper bounds to quantify the amount of multimodal interactions in this semi-supervised setting. We propose two lower bounds: one based on the shared information between modalities and the other based on disagreement between separately trained unimodal classifiers, and derive an upper bound through connections to approximate algorithms for min-entropy couplings. We validate these estimated bounds and show how they accurately track true interactions. Finally, we show how these theoretical results can be used to estimate multimodal model performance, guide data collection, and select appropriate multimodal models for various tasks.

cs.LG↗

arXiv2024

Online bipartite matching with imperfect advice

We study the problem of online unweighted bipartite matching with $n$ offline vertices and $n$ online vertices where one wishes to be competitive against the optimal offline algorithm. While the classic RANKING algorithm of Karp et al. [1990] provably attains competitive ratio of $1-1/e > 1/2$, we show that no learning-augmented method can be both 1-consistent and strictly better than $1/2$-robust under the adversarial arrival model. Meanwhile, under the random arrival model, we show how one can utilize methods from distribution testing to design an algorithm that takes in external advice about the online vertices and provably achieves competitive ratio interpolating between any ratio attainable by advice-free methods and the optimal ratio of 1, depending on the advice quality.

cs.LG↗

arXiv2024

Layered Graph Security Games

Security games model strategic interactions in adversarial real-world applications. Such applications often involve extremely large but highly structured strategy sets (e.g., selecting a distribution over all patrol routes in a given graph). In this paper, we represent each player's strategy space using a layered graph whose paths represent an exponentially large strategy space. Our formulation entails not only classic pursuit-evasion games, but also other security games, such as those modeling anti-terrorism and logistical interdiction. We study two-player zero-sum games under two distinct utility models: linear and binary utilities. We show that under linear utilities, Nash equilibrium can be computed in polynomial time, while binary utilities may lead to situations where even computing a best-response is computationally intractable. To this end, we propose a practical algorithm based on incremental strategy generation and mixed integer linear programs. We show through extensive experiments that our algorithm efficiently computes $ε$-equilibrium for many games of interest. We find that target values and graph structure often have a larger influence on running times as compared to the size of the graph per se.

cs.GT↗