Mustafa O. Karabag

Bo Chen, Calvin Hawkins, Mustafa O. Karabag et al.

Privacy-aware multiagent systems must protect agents' sensitive data while simultaneously ensuring that agents accomplish their shared objectives. Towards this goal, we propose a framework to privatize inter-agent communications in cooperative multiagent decision-making problems. We study sequential decision-making problems formulated as cooperative Markov games with reach-avoid objectives. We apply a differential privacy mechanism to privatize agents' communicated symbolic state trajectories, and then we analyze tradeoffs between the strength of privacy and the team's performance. For a given level of privacy, this tradeoff is shown to depend critically upon the total correlation among agents' state-action processes. We synthesize policies that are robust to privacy by reducing the value of the total correlation. Numerical experiments demonstrate that the team's performance under these policies decreases by only 3 percent when comparing private versus non-private implementations of communication. By contrast, the team's performance decreases by roughly 86 percent when using baseline policies that ignore total correlation and only optimize team performance.

Tichakorn Wongpiromsarn, Mahsa Ghasemi, Murat Cubuktepe et al.

Formal methods refer to rigorous, mathematical approaches to system development and have played a key role in establishing the correctness of safety-critical systems. The main building blocks of formal methods are models and specifications, which are analogous to behaviors and requirements in system design and give us the means to verify and synthesize system behaviors with formal guarantees. This monograph provides a survey of the current state of the art on applications of formal methods in the autonomous systems domain. We consider correct-by-construction synthesis under various formulations, including closed systems, reactive, and probabilistic settings. Beyond synthesizing systems in known environments, we address the concept of uncertainty and bound the behavior of systems that employ learning using formal methods. Further, we examine the synthesis of systems with monitoring, a mitigation technique for ensuring that once a system deviates from expected behavior, it knows a way of returning to normalcy. We also show how to overcome some limitations of formal methods themselves with learning. We conclude with future directions for formal methods in reinforcement learning, uncertainty, privacy, explainability of formal methods, and regulation and certification.

Shenghui Chen, Yagiz Savas, Mustafa O. Karabag et al.

We consider a team of autonomous agents that navigate in an adversarial environment and aim to achieve a task by allocating their resources over a set of target locations. An adversary in the environment observes the autonomous team's behavior to infer their objective and responds against the team. In this setting, we propose strategies for controlling the density of the autonomous team so that they can deceive the adversary regarding their objective while achieving the desired final resource allocation. We first develop a prediction algorithm based on the principle of maximum entropy to express the team's behavior expected by the adversary. Then, by measuring the deceptiveness via Kullback-Leibler divergence, we devise convex optimization-based planning algorithms that deceive the adversary by either exaggerating the behavior towards a decoy allocation strategy or creating ambiguity regarding the final allocation strategy. A user study with $320$ participants demonstrates that the proposed algorithms are effective for deception and reveal the inherent biases of participants towards proximate goals.

Mustafa O. Karabag, Ufuk Topcu

Offline reinforcement learning (offline RL) considers problems where learning is performed using only previously collected samples and is helpful for the settings in which collecting new data is costly or risky. In model-based offline RL, the learner performs estimation (or optimization) using a model constructed according to the empirical transition frequencies. We analyze the sample complexity of vanilla model-based offline RL with dependent samples in the infinite-horizon discounted-reward setting. In our setting, the samples obey the dynamics of the Markov decision process and, consequently, may have interdependencies. Under no assumption of independent samples, we provide a high-probability, polynomial sample complexity bound for vanilla model-based off-policy evaluation that requires partial or uniform coverage. We extend this result to the off-policy optimization under uniform coverage. As a comparison to the model-based approach, we analyze the sample complexity of off-policy evaluation with vanilla importance sampling in the infinite-horizon setting. Finally, we provide an estimator that outperforms the sample-mean estimator for almost deterministic dynamics that are prevalent in reinforcement learning.

Surya Murthy, Mustafa O. Karabag, Ufuk Topcu

Autonomous agents interact with other autonomous agents and humans of unknown preferences to share resources in their environment. We explore sequential trading for resource allocation in a setting where two greedily rational agents sequentially trade resources from a finite set of categories. Each agent has a utility function that depends on the amount of resources it possesses in each category. The offering agent makes trade offers to improve its utility without knowing the responding agent's utility function, and the responding agent only accepts offers that improve its utility. To facilitate cooperation between an autonomous agent and another autonomous agent or a human, we present an algorithm for the offering agent to estimate the responding agent's gradient (preferences) and make offers based on previous acceptance or rejection responses. The algorithm's goal is to reach a Pareto-optimal resource allocation state while ensuring that the utilities of both agents improve after every accepted trade. The algorithm estimates the responding agent's gradient by leveraging the rejected offers and the greedy rationality assumption, to prune the space of potential gradients. We show that, after the algorithm makes a finite number of rejected offers, the algorithm either finds a mutually beneficial trade or certifies that the current state is epsilon-weakly Pareto optimal. We compare the proposed algorithm against various baselines in continuous and discrete trading scenarios and show that it improves the societal benefit with fewer offers. Additionally, we validate these findings in a user study with human participants, where the algorithm achieves high performance in scenarios with high resource conflict due to aligned agent goals.

Mustafa O. Karabag, Sophia Smith, Negar Mehr et al.

When interacting with other decision-making agents in non-adversarial scenarios, it is critical for an autonomous agent to have inferable behavior: The agent's actions must convey their intention and strategy. We model the inferability problem using Stackelberg games with observations where a leader and a follower repeatedly interact. During the interactions, the leader uses a fixed mixed strategy. The follower does not know the leader's strategy and dynamically reacts to the statistically inferred strategy based on the leader's previous actions. In the inference setting, the leader may have a lower performance compared to the setting where the follower has full information on the leader's strategy. We refer to the performance gap between these settings as the inferability gap. For a variety of game settings, we show that the inferability gap is upper-bounded by a function of the number of interactions and the stochasticity level of the leader's strategy, encouraging the use of inferable strategies with lower stochasticity levels. We also analyze bimatrix Stackelberg games and identify a set of games where the leader's near-optimal strategy may potentially suffer from a large inferability gap.

Surya Murthy, Kushagra Gupta, Mustafa O. Karabag et al.

Multitask learning (MTL) algorithms typically rely on schemes that combine different task losses or their gradients through weighted averaging. These methods aim to find Pareto stationary points by using heuristics that require access to task loss values, gradients, or both. In doing so, a central challenge arises because task losses can be arbitrarily, nonaffinely scaled relative to one another, causing certain tasks to dominate training and degrade overall performance. A recent advance in cooperative bargaining theory, the Direction-based Bargaining Solution (DiBS), yields Pareto stationary solutions immune to task domination because of its invariance to monotonic nonaffine task loss transformations. However, the convergence behavior of DiBS in nonconvex MTL settings is currently not understood. To this end, we prove that under standard assumptions, a subsequence of DiBS iterates converges to a Pareto stationary point when task losses are possibly nonconvex, and propose DiBS-MTL, a computationally efficient adaptation of DiBS to the MTL setting. Finally, we validate DiBS-MTL empirically on standard MTL benchmarks, showing that it achieves competitive performance with state-of-the-art methods while maintaining robustness to nonaffine monotonic transformations that significantly degrade the performance of existing approaches, including prior bargaining-inspired MTL methods. Code available at https://github.com/suryakmurthy/dibs-mtl.

Jan Sobotka, Mustafa O. Karabag, Ufuk Topcu

Large language models (LLMs) are increasingly tasked with strategic decision-making under incomplete information, such as in negotiation and policymaking. While LLMs can excel at many such tasks, they also fail in ways that are poorly understood. We shed light on these failures by uncovering two fundamental gaps in the internal mechanisms underlying the decision-making of LLMs in incomplete-information games, supported by experiments with open-weight models Llama 3.1, Qwen3, and gpt-oss. First, an observation-belief gap: LLMs encode internal beliefs about latent game states that are substantially more accurate than their own verbal reports, yet these beliefs are brittle. In particular, the belief accuracy degrades with multi-hop reasoning, exhibits primacy and recency biases, and drifts away from Bayesian coherence over extended interactions. Second, a belief-action gap: The implicit conversion of internal beliefs into actions is weaker than that of the beliefs externalized in the prompt, yet neither belief-conditioning consistently achieves higher game payoffs. These results show how analyzing LLMs' internal processes can expose systematic vulnerabilities that warrant caution before deploying LLMs in strategic domains without robust guardrails.

Wesley A. Suttle, Jesse Milzman, Mustafa O. Karabag et al.

Existing methods for deceptive path planning (DPP) address the problem of designing paths that conceal their true goal from a passive, external observer. Such methods do not apply to problems where the observer has the ability to perform adversarial interventions to impede the path planning agent. In this paper, we propose a novel Markov decision process (MDP)-based model for the DPP problem under adversarial interventions and develop new value of information (VoI) objectives to guide the design of DPP policies. Using the VoI objectives we propose, path planning agents deceive the adversarial observer into choosing suboptimal interventions by selecting trajectories that are of low informational value to the observer. Leveraging connections to the linear programming theory for MDPs, we derive computationally efficient solution methods for synthesizing policies for performing DPP under adversarial interventions. In our experiments, we illustrate the effectiveness of the proposed solution method in achieving deceptiveness under adversarial interventions and demonstrate the superior performance of our approach to both existing DPP methods and conservative path planning approaches on illustrative gridworld problems.

Mustafa O. Karabag, Jan Sobotka, Ufuk Topcu

Large language model-based (LLM-based) agents have become common in settings that include non-cooperative parties. In such settings, agents' decision-making needs to conceal information from their adversaries, reveal information to their cooperators, and infer information to identify the other agents' characteristics. To investigate whether LLMs have these information control and decision-making capabilities, we make LLM agents play the language-based hidden-identity game, The Chameleon. In this game, a group of non-chameleon agents who do not know each other aim to identify the chameleon agent without revealing a secret. The game requires the aforementioned information control capabilities both as a chameleon and a non-chameleon. We begin with a theoretical analysis for a spectrum of strategies, from concealing to revealing, and provide bounds on the non-chameleons' winning probability. The empirical results with GPT, Gemini 2.5 Pro, Llama 3.1, and Qwen3 models show that while non-chameleon LLM agents identify the chameleon, they fail to conceal the secret from the chameleon, and their winning probability is far from the levels of even trivial strategies. Based on these empirical results and our theoretical analysis, we deduce that LLM-based agents may reveal excessive information to agents of unknown identities. Interestingly, we find that, when instructed to adopt an information-revealing level, this level is linearly encoded in the LLM's internal representations. While the instructions alone are often ineffective at making non-chameleon LLMs conceal, we show that steering the internal representations in this linear direction directly can reliably induce concealing behavior.

I. Arda Vurankaya, Mustafa O. Karabag, Wesley A. Suttle et al.

We consider a multi-armed bandit setting in which each arm has a public and a private reward distribution. An observer expects an agent to follow Thompson Sampling according to the public rewards, however, the deceptive agent aims to quickly identify the best private arm without being noticed. The observer can observe the public rewards and the pulled arms, but not the private rewards. The agent, on the other hand, observes both the public and private rewards. We formalize detectability as a stepwise Kullback-Leibler (KL) divergence constraint between the actual pull probabilities used by the agent and the anticipated pull probabilities by the observer. We model successful pulling of public suboptimal arms as a % Bernoulli process where the success probability decreases with each successful pull, and show these pulls can happen at most at a $Θ(\sqrt{T}) $ rate under the KL constraint. We then formulate a maximin problem based on public and private means, whose solution characterizes the optimal error exponent for best private arm identification. We finally propose an algorithm inspired by top-two algorithms. This algorithm naturally adapts its exploration according to the hardness of pulling arms based on the public suboptimality gaps. We provide numerical examples illustrating the $Θ(\sqrt{T}) $ rate and the behavior of the proposed algorithm.

Mustafa O. Karabag, Cyrus Neary, Ufuk Topcu

In a cooperative multiagent system, a collection of agents executes a joint policy in order to achieve some common objective. The successful deployment of such systems hinges on the availability of reliable inter-agent communication. However, many sources of potential disruption to communication exist in practice, such as radio interference, hardware failure, and adversarial attacks. In this work, we develop joint policies for cooperative multiagent systems that are robust to potential losses in communication. More specifically, we develop joint policies for cooperative Markov games with reach-avoid objectives. First, we propose an algorithm for the decentralized execution of joint policies during periods of communication loss. Next, we use the total correlation of the state-action process induced by a joint policy as a measure of the intrinsic dependencies between the agents. We then use this measure to lower-bound the performance of a joint policy when communication is lost. Finally, we present an algorithm that maximizes a proxy to this lower bound in order to synthesize minimum-dependency joint policies that are robust to communication loss. Numerical experiments show that the proposed minimum-dependency policies require minimal coordination between the agents while incurring little to no loss in performance; the total correlation value of the synthesized policy is one fifth of the total correlation value of the baseline policy which does not take potential communication losses into account. As a result, the performance of the minimum-dependency policies remains consistently high regardless of whether or not communication is available. By contrast, the performance of the baseline policy decreases by twenty percent when communication is lost.

Yagiz Savas, Melkior Ornik, Murat Cubuktepe et al.

We study the problem of synthesizing a policy that maximizes the entropy of a Markov decision process (MDP) subject to a temporal logic constraint. Such a policy minimizes the predictability of the paths it generates, or dually, maximizes the exploration of different paths in an MDP while ensuring the satisfaction of a temporal logic specification. We first show that the maximum entropy of an MDP can be finite, infinite or unbounded. We provide necessary and sufficient conditions under which the maximum entropy of an MDP is finite, infinite or unbounded. We then present an algorithm which is based on a convex optimization problem to synthesize a policy that maximizes the entropy of an MDP. We also show that maximizing the entropy of an MDP is equivalent to maximizing the entropy of the paths that reach a certain set of states in the MDP. Finally, we extend the algorithm to an MDP subject to a temporal logic specification. In numerical examples, we demonstrate the proposed method on different motion planning scenarios and illustrate the relation between the restrictions imposed on the paths by a specification, the maximum entropy, and the predictability of paths.