Michael Dorothy

Yue Guan, Daigo Shishika, Jason R. Marden et al. · gatech

This work introduces the dynamic Defender-Attacker Blotto (dDAB) game, extending the classical static Blotto game to a dynamic resource allocation setting over graphs. In the dDAB game, a defender is required to maintain numerical superiority against attacker resources across a set of key nodes in a connected graph. The engagement unfolds as a discrete-time game, where each player reallocates its resources in turn, with resources allowed to move at most one hop per time step. The primary goal is to determine the necessary and sufficient amount of defender resources required to guarantee sustained defense, along with the corresponding strategies. To address the central challenge arising from graph-constrained resource reallocation, we conduct a reachability analysis, starting with simplified settings where attacker resources act as a single cohesive group. We then extend the framework to allow attacker resources to split and merge arbitrarily, and construct defender strategies using superposition principles. A set-based dynamic programming algorithm is developed to compute the optimal strategies, as well as the minimum amount of defender resources to ensure successful defense. The effectiveness of our approach is demonstrated through numerical simulations and hardware experiments on the Georgia Tech Robotarium platform.

Derrik E. Asher, Anjon Basak, Rolando Fernandez et al.

Reinforcement learning (RL) approaches can illuminate emergent behaviors that facilitate coordination across teams of agents as part of a multi-agent system (MAS), which can provide windows of opportunity in various military tasks. Technologically advancing adversaries pose substantial risks to a friendly nation's interests and resources. Superior resources alone are not enough to defeat adversaries in modern complex environments because adversaries create standoff in multiple domains against predictable military doctrine-based maneuvers. Therefore, as part of a defense strategy, friendly forces must use strategic maneuvers and disruption to gain superiority in complex multi-faceted domains such as multi-domain operations (MDO). One promising avenue for implementing strategic maneuver and disruption to gain superiority over adversaries is through coordination of MAS in future military operations. In this paper, we present overviews of prominent works in the RL domain with their strengths and weaknesses for overcoming the challenges associated with performing autonomous strategic maneuver and disruption in military contexts.

Prajakta Surve, Shaunak D. Bopardikar, Daigo Shishika et al.

We consider a hide-and-seek game between a Hider and a Seeker over a finite set of locations. The Hider chooses one location to conceal a stationary treasure, while the Seeker visits the locations sequentially along a route. As the search progresses, the Hider observes a prefix of the Seeker's route. After observing this information, the Hider has the option to relocate the treasure at most once to another unvisited location by paying a switching cost. We study two seeker models. In the first, the Seeker is unaware of the fact that the Hider can relocate. In the second, the Seeker select its route while accounting for the possibility that the Hider observes its path and reallocates. For the restricted case, we define the value-of-information created by the reveal and derive upper bounds in terms of the switching cost using a worst-case evaluation over routes. We also show that seeker awareness reduces the game value, with the difference between the restricted and feedback models bounded by the entry-wise gap between the corresponding payoff matrices. Numerical examples show how this benefit decreases as the switching cost increases and as the reveal occurs later along the route.

Goutam Das, Michael Dorothy, Kyle Volle et al.

Game theory provides the gold standard for analyzing adversarial engagements, offering strong optimality guarantees. However, these guarantees often become brittle when assumptions such as perfect information are violated. Reinforcement learning (RL), by contrast, is adaptive but can be sample-inefficient in large, complex domains. This paper introduces a hybrid approach that leverages game-theoretic insights to improve RL training efficiency. We study a border defense game with limited perceptual range, where defender performance depends on both search and pursuit strategies, making classical differential game solutions inapplicable. Our method employs the Apollonius Circle (AC) to compute equilibrium in the post-detection phase, enabling early termination of RL episodes without learning pursuit dynamics. This allows RL to concentrate on learning search strategies while guaranteeing optimal continuation after detection. Across single- and multi-defender settings, this early termination method yields 10-20% higher rewards, faster convergence, and more efficient search trajectories. Extensive experiments validate these findings and demonstrate the overall effectiveness of our approach.

Haoxiang Ma, Chongyang Shi, Shuo Han et al.

Covert planning refers to a class of constrained planning problems where an agent aims to accomplish a task with minimal information leaked to a passive observer to avoid detection. However, existing methods of covert planning often consider deterministic environments or do not exploit the observer's imperfect information. This paper studies how covert planning can leverage the coupling of stochastic dynamics and the observer's imperfect observation to achieve optimal task performance without being detected. Specifically, we employ a Markov decision process to model the interaction between the agent and its stochastic environment, and a partial observation function to capture the leaked information to a passive observer. Assuming the observer employs hypothesis testing to detect if the observation deviates from a nominal policy, the covert planning agent aims to maximize the total discounted reward while keeping the probability of being detected as an adversary below a given threshold. We prove that finite-memory policies are more powerful than Markovian policies in covert planning. Then, we develop a primal-dual proximal policy gradient method with a two-time-scale update to compute a (locally) optimal covert policy. We demonstrate the effectiveness of our methods using a stochastic gridworld example. Our experimental results illustrate that the proposed method computes a policy that maximizes the adversary's expected reward without violating the detection constraint, and empirically demonstrates how the environmental noises can influence the performance of the covert policies.

Chongyang Shi, Michael Dorothy, Jie Fu

We study the policy synthesis problem in contextual partially observable Markov decision processes (CPOMDPs), where the environment is governed by an unknown latent context that induces distinct POMDP dynamics. Our goal is to design a policy that simultaneously maximizes cumulative return and actively reduces uncertainty about the underlying context. We introduce an information-directed objective that augments reward maximization with mutual information between the latent context and the agent's observations. We develop the C-IDS algorithm to synthesize policies that maximize the information-directed objective. We show that the objective can be interpreted as a Lagrangian relaxation of the linear information ratio and prove that the temperature parameter is an upper bound on the information ratio. Based on this characterization, we establish a sublinear Bayesian regret bound over K episodes. We evaluate our approach on a continuous Light-Dark environment and show that it consistently outperforms standard POMDP solvers that treat the unknown context as a latent state variable, achieving faster context identification and higher returns.