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Adam Wierman

Publications and source records attributed to Adam Wierman.

At least 73 records · Page 4Linked to original sources
arXiv2024

Characterizing Controllability and Observability for Systems with Locality, Communication, and Actuation Constraints

This paper presents a closed-form notion of controllability and observability for systems with communication delays, actuation delays, and locality constraints. The formulation reduces to classical notions of controllability and observability in the unconstrained setting. As a consequence of our formulation, we show that the addition of locality and communication constraints may not affect the controllability and observability of the system, and we provide an efficient sufficient condition under which this phenomenon occurs. This contrasts with actuation and sensing delays, which cause a gradual loss of controllability and observability as the delays increase. We illustrate our results using linearized swing equations for the power grid, showing how actuation delay and locality constraints affect controllability.

math.OC↗
arXiv2024

Best of Both Worlds Guarantees for Smoothed Online Quadratic Optimization

We study the smoothed online quadratic optimization (SOQO) problem where, at each round $t$, a player plays an action $x_t$ in response to a quadratic hitting cost and an additional squared $\ell_2$-norm cost for switching actions. This problem class has strong connections to a wide range of application domains including smart grid management, adaptive control, and data center management, where switching-efficient algorithms are highly sought after. We study the SOQO problem in both adversarial and stochastic settings, and in this process, perform the first stochastic analysis of this class of problems. We provide the online optimal algorithm when the minimizers of the hitting cost function evolve as a general stochastic process, which, for the case of martingale process, takes the form of a distribution-agnostic dynamic interpolation algorithm (LAI). Next, we present the stochastic-adversarial trade-off by proving an $Ω(T)$ expected regret for the adversarial optimal algorithm in the literature (ROBD) with respect to LAI and, a sub-optimal competitive ratio for LAI in the adversarial setting. Finally, we present a best-of-both-worlds algorithm that obtains a robust adversarial performance while simultaneously achieving a near-optimal stochastic performance.

math.OC↗
arXiv2024

Anytime-Competitive Reinforcement Learning with Policy Prior

This paper studies the problem of Anytime-Competitive Markov Decision Process (A-CMDP). Existing works on Constrained Markov Decision Processes (CMDPs) aim to optimize the expected reward while constraining the expected cost over random dynamics, but the cost in a specific episode can still be unsatisfactorily high. In contrast, the goal of A-CMDP is to optimize the expected reward while guaranteeing a bounded cost in each round of any episode against a policy prior. We propose a new algorithm, called Anytime-Competitive Reinforcement Learning (ACRL), which provably guarantees the anytime cost constraints. The regret analysis shows the policy asymptotically matches the optimal reward achievable under the anytime competitive constraints. Experiments on the application of carbon-intelligent computing verify the reward performance and cost constraint guarantee of ACRL.

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arXiv2023

Online Stabilization of Unknown Linear Time-Varying Systems

This paper studies the problem of online stabilization of an unknown discrete-time linear time-varying (LTV) system under bounded non-stochastic (potentially adversarial) disturbances. We propose a novel control algorithm based on convex body chasing (CBC). Under the assumption of infrequently changing or slowly drifting dynamics, the algorithm guarantees bounded-input-bounded-output stability in the closed loop. Our approach avoids system identification and applies, with minimal disturbance assumptions, to a variety of LTV systems of practical importance. We demonstrate the algorithm numerically on examples of LTV systems including Markov linear jump systems with finitely many jumps.

math.OC↗
arXiv2023

Two-Timescale Q-Learning with Function Approximation in Zero-Sum Stochastic Games

We consider two-player zero-sum stochastic games and propose a two-timescale $Q$-learning algorithm with function approximation that is payoff-based, convergent, rational, and symmetric between the two players. In two-timescale $Q$-learning, the fast-timescale iterates are updated in spirit to the stochastic gradient descent and the slow-timescale iterates (which we use to compute the policies) are updated by taking a convex combination between its previous iterate and the latest fast-timescale iterate. Introducing the slow timescale as well as its update equation marks as our main algorithmic novelty. In the special case of linear function approximation, we establish, to the best of our knowledge, the first last-iterate finite-sample bound for payoff-based independent learning dynamics of these types. The result implies a polynomial sample complexity to find a Nash equilibrium in such stochastic games. To establish the results, we model our proposed algorithm as a two-timescale stochastic approximation and derive the finite-sample bound through a Lyapunov-based approach. The key novelty lies in constructing a valid Lyapunov function to capture the evolution of the slow-timescale iterates. Specifically, through a change of variable, we show that the update equation of the slow-timescale iterates resembles the classical smoothed best-response dynamics, where the regularized Nash gap serves as a valid Lyapunov function. This insight enables us to construct a valid Lyapunov function via a generalized variant of the Moreau envelope of the regularized Nash gap. The construction of our Lyapunov function might be of broad independent interest in studying the behavior of stochastic approximation algorithms.

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arXiv2023

Adversarial Attacks on Cooperative Multi-agent Bandits

Cooperative multi-agent multi-armed bandits (CMA2B) consider the collaborative efforts of multiple agents in a shared multi-armed bandit game. We study latent vulnerabilities exposed by this collaboration and consider adversarial attacks on a few agents with the goal of influencing the decisions of the rest. More specifically, we study adversarial attacks on CMA2B in both homogeneous settings, where agents operate with the same arm set, and heterogeneous settings, where agents have distinct arm sets. In the homogeneous setting, we propose attack strategies that, by targeting just one agent, convince all agents to select a particular target arm $T-o(T)$ times while incurring $o(T)$ attack costs in $T$ rounds. In the heterogeneous setting, we prove that a target arm attack requires linear attack costs and propose attack strategies that can force a maximum number of agents to suffer linear regrets while incurring sublinear costs and only manipulating the observations of a few target agents. Numerical experiments validate the effectiveness of our proposed attack strategies.

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arXiv2023

Robust Learning for Smoothed Online Convex Optimization with Feedback Delay

We study a challenging form of Smoothed Online Convex Optimization, a.k.a. SOCO, including multi-step nonlinear switching costs and feedback delay. We propose a novel machine learning (ML) augmented online algorithm, Robustness-Constrained Learning (RCL), which combines untrusted ML predictions with a trusted expert online algorithm via constrained projection to robustify the ML prediction. Specifically,we prove that RCL is able to guarantee$(1+λ)$-competitiveness against any given expert for any$λ>0$, while also explicitly training the ML model in a robustification-aware manner to improve the average-case performance. Importantly,RCL is the first ML-augmented algorithm with a provable robustness guarantee in the case of multi-step switching cost and feedback delay.We demonstrate the improvement of RCL in both robustness and average performance using battery management for electrifying transportationas a case study.

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arXiv2023

Stability Constrained Reinforcement Learning for Decentralized Real-Time Voltage Control

Deep reinforcement learning has been recognized as a promising tool to address the challenges in real-time control of power systems. However, its deployment in real-world power systems has been hindered by a lack of explicit stability and safety guarantees. In this paper, we propose a stability-constrained reinforcement learning (RL) method for real-time voltage control, that guarantees system stability both during policy learning and deployment of the learned policy. The key idea underlying our approach is an explicitly constructed Lyapunov function that leads to a sufficient structural condition for stabilizing policies, i.e., monotonically decreasing policies guarantee stability. We incorporate this structural constraint with RL, by parameterizing each local voltage controller using a monotone neural network, thus ensuring the stability constraint is satisfied by design. We demonstrate the effectiveness of our approach in both single-phase and three-phase IEEE test feeders, where the proposed method can reduce the transient control cost by more than 25% and shorten the voltage recovery time by 21.5% on average compared to the widely used linear policy, while always achieving voltage stability. In contrast, standard RL methods often fail to achieve voltage stability.

eess.SY↗
arXiv2023

Beyond Black-Box Advice: Learning-Augmented Algorithms for MDPs with Q-Value Predictions

We study the tradeoff between consistency and robustness in the context of a single-trajectory time-varying Markov Decision Process (MDP) with untrusted machine-learned advice. Our work departs from the typical approach of treating advice as coming from black-box sources by instead considering a setting where additional information about how the advice is generated is available. We prove a first-of-its-kind consistency and robustness tradeoff given Q-value advice under a general MDP model that includes both continuous and discrete state/action spaces. Our results highlight that utilizing Q-value advice enables dynamic pursuit of the better of machine-learned advice and a robust baseline, thus result in near-optimal performance guarantees, which provably improves what can be obtained solely with black-box advice.

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arXiv2023

Convergence Rates for Localized Actor-Critic in Networked Markov Potential Games

We introduce a class of networked Markov potential games in which agents are associated with nodes in a network. Each agent has its own local potential function, and the reward of each agent depends only on the states and actions of the agents within a neighborhood. In this context, we propose a localized actor-critic algorithm. The algorithm is scalable since each agent uses only local information and does not need access to the global state. Further, the algorithm overcomes the curse of dimensionality through the use of function approximation. Our main results provide finite-sample guarantees up to a localization error and a function approximation error. Specifically, we achieve an $\tilde{\mathcal{O}}(\tildeε^{-4})$ sample complexity measured by the averaged Nash regret. This is the first finite-sample bound for multi-agent competitive games that does not depend on the number of agents.

cs.LG↗
arXiv2023

Online Adaptive Policy Selection in Time-Varying Systems: No-Regret via Contractive Perturbations

We study online adaptive policy selection in systems with time-varying costs and dynamics. We develop the Gradient-based Adaptive Policy Selection (GAPS) algorithm together with a general analytical framework for online policy selection via online optimization. Under our proposed notion of contractive policy classes, we show that GAPS approximates the behavior of an ideal online gradient descent algorithm on the policy parameters while requiring less information and computation. When convexity holds, our algorithm is the first to achieve optimal policy regret. When convexity does not hold, we provide the first local regret bound for online policy selection. Our numerical experiments show that GAPS can adapt to changing environments more quickly than existing benchmarks.

math.OC↗
arXiv2023

Adversarial Attacks on Online Learning to Rank with Click Feedback

Online learning to rank (OLTR) is a sequential decision-making problem where a learning agent selects an ordered list of items and receives feedback through user clicks. Although potential attacks against OLTR algorithms may cause serious losses in real-world applications, little is known about adversarial attacks on OLTR. This paper studies attack strategies against multiple variants of OLTR. Our first result provides an attack strategy against the UCB algorithm on classical stochastic bandits with binary feedback, which solves the key issues caused by bounded and discrete feedback that previous works can not handle. Building on this result, we design attack algorithms against UCB-based OLTR algorithms in position-based and cascade models. Finally, we propose a general attack strategy against any algorithm under the general click model. Each attack algorithm manipulates the learning agent into choosing the target attack item $T-o(T)$ times, incurring a cumulative cost of $o(T)$. Experiments on synthetic and real data further validate the effectiveness of our proposed attack algorithms.

cs.LG↗
arXiv2023

The Online Pause and Resume Problem: Optimal Algorithms and An Application to Carbon-Aware Load Shifting

We introduce and study the online pause and resume problem. In this problem, a player attempts to find the $k$ lowest (alternatively, highest) prices in a sequence of fixed length $T$, which is revealed sequentially. At each time step, the player is presented with a price and decides whether to accept or reject it. The player incurs a switching cost whenever their decision changes in consecutive time steps, i.e., whenever they pause or resume purchasing. This online problem is motivated by the goal of carbon-aware load shifting, where a workload may be paused during periods of high carbon intensity and resumed during periods of low carbon intensity and incurs a cost when saving or restoring its state. It has strong connections to existing problems studied in the literature on online optimization, though it introduces unique technical challenges that prevent the direct application of existing algorithms. Extending prior work on threshold-based algorithms, we introduce double-threshold algorithms for both the minimization and maximization variants of this problem. We further show that the competitive ratios achieved by these algorithms are the best achievable by any deterministic online algorithm. Finally, we empirically validate our proposed algorithm through case studies on the application of carbon-aware load shifting using real carbon trace data and existing baseline algorithms.

cs.DS↗
arXiv2023

The Online Knapsack Problem with Departures

The online knapsack problem is a classic online resource allocation problem in networking and operations research. Its basic version studies how to pack online arriving items of different sizes and values into a capacity-limited knapsack. In this paper, we study a general version that includes item departures, while also considering multiple knapsacks and multi-dimensional item sizes. We design a threshold-based online algorithm and prove that the algorithm can achieve order-optimal competitive ratios. Beyond worst-case performance guarantees, we also aim to achieve near-optimal average performance under typical instances. Towards this goal, we propose a data-driven online algorithm that learns within a policy-class that guarantees a worst-case performance bound. In trace-driven experiments, we show that our data-driven algorithm outperforms other benchmark algorithms in an application of online knapsack to job scheduling for cloud computing.

cs.DS↗
arXiv2023

A Finite-Sample Analysis of Payoff-Based Independent Learning in Zero-Sum Stochastic Games

We study two-player zero-sum stochastic games, and propose a form of independent learning dynamics called Doubly Smoothed Best-Response dynamics, which integrates a discrete and doubly smoothed variant of the best-response dynamics into temporal-difference (TD)-learning and minimax value iteration. The resulting dynamics are payoff-based, convergent, rational, and symmetric among players. Our main results provide finite-sample guarantees. In particular, we prove the first-known $\tilde{\mathcal{O}}(1/ε^2)$ sample complexity bound for payoff-based independent learning dynamics, up to a smoothing bias. In the special case where the stochastic game has only one state (i.e., matrix games), we provide a sharper $\tilde{\mathcal{O}}(1/ε)$ sample complexity. Our analysis uses a novel coupled Lyapunov drift approach to capture the evolution of multiple sets of coupled and stochastic iterates, which might be of independent interest.

cs.GT↗
arXiv2023

Online switching control with stability and regret guarantees

This paper considers online switching control with a finite candidate controller pool, an unknown dynamical system, and unknown cost functions. The candidate controllers can be unstabilizing policies. We only require at least one candidate controller to satisfy certain stability properties, but we do not know which one is stabilizing. We design an online algorithm that guarantees finite-gain stability throughout the duration of its execution. We also provide a sublinear policy regret guarantee compared with the optimal stabilizing candidate controller. Lastly, we numerically test our algorithm on quadrotor planar flights and compare it with a classical switching control algorithm, falsification-based switching, and a classical multi-armed bandit algorithm, Exp3 with batches.

math.OC↗
arXiv2023

Online Adversarial Stabilization of Unknown Networked Systems

We investigate the problem of stabilizing an unknown networked linear system under communication constraints and adversarial disturbances. We propose the first provably stabilizing algorithm for the problem. The algorithm uses a distributed version of nested convex body chasing to maintain a consistent estimate of the network dynamics and applies system level synthesis to determine a distributed controller based on this estimated model. Our approach avoids the need for system identification and accommodates a broad class of communication delay while being fully distributed and scaling favorably with the number of subsystems.

eess.SY↗
arXiv2022

Global Convergence of Localized Policy Iteration in Networked Multi-Agent Reinforcement Learning

We study a multi-agent reinforcement learning (MARL) problem where the agents interact over a given network. The goal of the agents is to cooperatively maximize the average of their entropy-regularized long-term rewards. To overcome the curse of dimensionality and to reduce communication, we propose a Localized Policy Iteration (LPI) algorithm that provably learns a near-globally-optimal policy using only local information. In particular, we show that, despite restricting each agent's attention to only its $κ$-hop neighborhood, the agents are able to learn a policy with an optimality gap that decays polynomially in $κ$. In addition, we show the finite-sample convergence of LPI to the global optimal policy, which explicitly captures the trade-off between optimality and computational complexity in choosing $κ$. Numerical simulations demonstrate the effectiveness of LPI.

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