Calvin Hawkins

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.

Joshua Kartzman, Calvin Hawkins, Matthew Hale

This paper considers the constrained sampling multi-stream quickest change detection problem, also known as the bandit quickest change detection problem. One stream contains a change-point that shifts its mean by an unknown amount. The goal is to quickly detect this change while controlling for false alarms, while being only able to sample one stream at each time. We propose an algorithm that combines a decaying-$ε$-greedy stream switching rule with a Generalized Likelihood Ratio detection procedure for unknown post-change means. We provide performance bounds for our algorithm and show it achieves approximate asymptotic first-order optimality with respect to a commonly used surrogate. We are the first to provide guarantees in this setting without assumptions such as a discretized post-change parameter set or a lower bound on the magnitude of change. We provide guarantees for a wide range of light-tailed distributions, including sub-Gaussian and bounded support distributions.

Ehsan Asadollahi, Calvin Hawkins, Matthew Hale

We study repeated multi-player vector-valued games in which a player observes a payoff vector each round and evaluates outcomes through linear scalarizations of those vectors. Different from most prior works, the choice of scalarization is treated as an online decision variable rather than a fixed modeling decision. We propose a bi-level learning framework in which an outer learner chooses a scalarization from a finite candidate class on a slow timescale, while a faster inner bandit no-regret learner selects actions using the scalar feedback induced by the chosen scalarization. Performance of this approach is defined with respect to a certain true weight vector, and the deployed scalarizations act as control signals that shape the induced payoff trajectory. We provide implementable algorithms based on bandit online mirror descent with stabilized importance weighting, and we derive finite-time performance guarantees in the form of sublinear regret bounds. Experiments on a vector-valued extension of a canonical game show that convergence to the preferred equilibrium rises from roughly $50\%$ under non-adaptive scalarization to about $80\%$ under our proposed method.

Bo Chen, Calvin Hawkins, Kasra Yazdani et al.

Graphs are the dominant formalism for modeling multi-agent systems. The algebraic connectivity of a graph is particularly important because it provides the convergence rates of consensus algorithms that underlie many multi-agent control and optimization techniques. However, sharing the value of algebraic connectivity can inadvertently reveal sensitive information about the topology of a graph, such as connections in social networks. Therefore, in this work we present a method to release a graph's algebraic connectivity under a graph-theoretic form of differential privacy, called edge differential privacy. Edge differential privacy obfuscates differences among graphs' edge sets and thus conceals the absence or presence of sensitive connections therein. We provide privacy with bounded Laplace noise, which improves accuracy relative to conventional unbounded noise. The private algebraic connectivity values are analytically shown to provide accurate estimates of consensus convergence rates, as well as accurate bounds on the diameter of a graph and the mean distance between its nodes. Simulation results confirm the utility of private algebraic connectivity in these contexts.

Calvin Hawkins, Matthew Hale

As multi-agent systems proliferate, there is increasing demand for coordination protocols that protect agents' sensitive information while allowing them to collaborate. To help address this need, this paper presents a differentially private formation control framework. Agents' state trajectories are protected using differential privacy, which is a statistical notion of privacy that protects data by adding noise to it. We provide a private formation control implementation and analyze the impact of privacy upon the system. Specifically, we quantify tradeoffs between privacy level, system performance, and connectedness of the network's communication topology. These tradeoffs are used to develop guidelines for calibrating privacy in terms of control theoretic quantities, such as steady-state error, without requiring in-depth knowledge of differential privacy. Additional guidelines are also developed for treating privacy levels and network topologies as design parameters to tune the network's performance. Simulation results illustrate these tradeoffs and show that strict privacy is inherently compatible with strong system performance.