Zhan Gao

Jasmine Bayrooti, Zhan Gao, Amanda Prorok

Cooperative decentralized learning relies on direct information exchange between communicating agents, each with access to locally available datasets. The goal is to agree on model parameters that are optimal over all data. However, sharing parameters with untrustworthy neighbors can incur privacy risks by leaking exploitable information. To enable trustworthy cooperative learning, we propose a framework that embeds differential privacy into decentralized deep learning and secures each agent's local dataset during and after cooperative training. We prove convergence guarantees for algorithms derived from this framework and demonstrate its practical utility when applied to subgradient and ADMM decentralized approaches, finding accuracies approaching the centralized baseline while ensuring individual data samples are resilient to inference attacks. Furthermore, we study the relationships between accuracy, privacy budget, and networks' graph properties on collaborative classification tasks, discovering a useful invariance to the communication graph structure beyond a threshold.

Zhan Gao, Amanda Prorok

Traditional approaches to the design of multi-agent navigation algorithms consider the environment as a fixed constraint, despite the influence of spatial constraints on agents' performance. Yet hand-designing conducive environment layouts is inefficient and potentially expensive. The goal of this paper is to consider the environment as a decision variable in a system-level optimization problem, where both agent performance and environment cost are incorporated. Towards this end, we propose novel problems of unprioritized and prioritized environment optimization, where the former considers agents unbiasedly and the latter accounts for agent priorities. We show, through formal proofs, under which conditions the environment can change while guaranteeing completeness (i.e., all agents reach goals), and analyze the role of agent priorities in the environment optimization. We proceed to impose real-world constraints on the environment optimization and formulate it mathematically as a constrained stochastic optimization problem. Since the relation between agents, environment and performance is challenging to model, we leverage reinforcement learning to develop a model-free solution and a primal-dual mechanism to handle constraints. Distinct information processing architectures are integrated for various implementation scenarios, including online/offline optimization and discrete/continuous environment. Numerical results corroborate the theory and demonstrate the validity and adaptability of our approach.

Zhan Gao, Elvin Isufi

Stochastic graph neural networks (SGNNs) are information processing architectures that learn representations from data over random graphs. SGNNs are trained with respect to the expected performance, which comes with no guarantee about deviations of particular output realizations around the optimal expectation. To overcome this issue, we propose a variance-constrained optimization problem for SGNNs, balancing the expected performance and the stochastic deviation. An alternating primal-dual learning procedure is undertaken that solves the problem by updating the SGNN parameters with gradient descent and the dual variable with gradient ascent. To characterize the explicit effect of the variance-constrained learning, we conduct a theoretical analysis on the variance of the SGNN output and identify a trade-off between the stochastic robustness and the discrimination power. We further analyze the duality gap of the variance-constrained optimization problem and the converging behavior of the primal-dual learning procedure. The former indicates the optimality loss induced by the dual transformation and the latter characterizes the limiting error of the iterative algorithm, both of which guarantee the performance of the variance-constrained learning. Through numerical simulations, we corroborate our theoretical findings and observe a strong expected performance with a controllable standard deviation.

Zhan Gao, Alec Koppel, Alejandro Ribeiro

Stochastic gradient descent is a canonical tool for addressing stochastic optimization problems, and forms the bedrock of modern machine learning and statistics. In this work, we seek to balance the fact that attenuating step-size is required for exact asymptotic convergence with the fact that constant step-size learns faster in finite time up to an error. To do so, rather than fixing the mini-batch and the step-size at the outset, we propose a strategy to allow parameters to evolve adaptively. Specifically, the batch-size is set to be a piecewise-constant increasing sequence where the increase occurs when a suitable error criterion is satisfied. Moreover, the step-size is selected as that which yields the fastest convergence. The overall algorithm, two scale adaptive (TSA) scheme, is developed for both convex and non-convex stochastic optimization problems. It inherits the exact asymptotic convergence of stochastic gradient method. More importantly, the optimal error decreasing rate is achieved theoretically, as well as an overall reduction in computational cost. Experimentally, we observe that TSA attains a favorable tradeoff relative to standard SGD that fixes the mini-batch and the step-size, or simply allowing one to increase or decrease respectively.