Predictive online convex optimization

Lesage‐Landry, Antoine; Shames, Iman; Taylor, Joshua A.

doi:10.1016/j.automatica.2019.108771

Cited by 23 publications

(15 citation statements)

References 15 publications

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“…We use ONM to track the target's location in real-time. No other online convex optimization algorithms can guarantee performance on nonconvex loss functions like (22). We compare ONM with OGD [7].…”

Section: Examplementioning

confidence: 99%

Second-order Online Nonconvex Optimization

Lesage-Landry,

Taylor,

Shames

2020

Preprint

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We present the online Newton's method, a single-step second-order method for online nonconvex optimization. We analyze its performance and obtain a dynamic regret bound that is linear in the cumulative variation between round optima. We show that if the variation between round optima is limited, the method leads to a constant regret bound. In the general case, the online Newton's method outperforms online convex optimization algorithms for convex functions and performs similarly to a specialized algorithm for strongly convex functions. We simulate the performance of the online Newton's method on a nonlinear, nonconvex moving target localization example and find that it outperforms a first-order approach.

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Section: Examplementioning

confidence: 99%

Second-order Online Nonconvex Optimization

Lesage-Landry,

Taylor,

Shames

2020

Preprint

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“…The use of online learning methods for controlling dynamical systems has captured increasing attention from both the learning and control communities. Significant effort has been made to design online optimal controllers using tools from machine learning in a variety of contexts in recent years [7,9,12,13,31,48,49]. One general dynamic model of particular interest for many applications is the following, which has time-varying and time-coupling constraints:…”

Section: Introductionmentioning

confidence: 99%

“…In [9], the dynamic regret is bounded by ( Δ( )) and the constraint violations are bounded by ( 3/4 Δ( ) 1/4 ) where Δ( ) is the "drift" of the sequence of optimal actions. In [31], ( √ ) regret is proven, and the results are extended to incorporate future information (predictions). In the case of stochastic long-term constraints, the authors in [49] achieve ( √ log ) regret and constraint violations with high probability.…”

Section: Introductionmentioning

confidence: 99%

Information Aggregation for Constrained Online Control

Chen

Sun

et al. 2021

Proc. ACM Meas. Anal. Comput. Syst.

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This paper considers an online control problem involving two controllers. A central controller chooses an action from a feasible set that is determined by time-varying and coupling constraints, which depend on all past actions and states. The central controller's goal is to minimize the cumulative cost; however, the controller has access to neither the feasible set nor the dynamics directly, which are determined by a remote local controller. Instead, the central controller receives only an aggregate summary of the feasibility information from the local controller, which does not know the system costs. We show that it is possible for an online algorithm using feasibility information to nearly match the dynamic regret of an online algorithm using perfect information whenever the feasible sets satisfy a causal invariance criterion and there is a sufficiently large prediction window size. To do so, we use a form of feasibility aggregation based on entropic maximization in combination with a novel online algorithm, named Penalized Predictive Control (PPC) and demonstrate that aggregated information can be efficiently learned using reinforcement learning algorithms. The effectiveness of our approach for closed-loop coordination between central and local controllers is validated via an electric vehicle charging application in power systems.

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“…Time varying optimization problems are well studied, frequently under the name Online Convex Optimization or OCO [3] [4]. A predictive/corrective method for OCO is presented in [5], using gradient information and line search methods. Online convex optimisation with constraints is addressed by [9], with regret bounds and convergence results.…”

Section: Introductionmentioning

confidence: 99%

Optimization with Zeroth-Order Oracles in Formation

Elad¹,

Zelazo²,

Wood³

et al. 2020

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In this paper, we consider the optimisation of time varying functions by a network of agents with no gradient information. The proposed a novel method to estimate the gradient at each agent's position using only neighbour information. The gradient estimation is coupled with a formation controller, to minimise gradient estimation error and prevent agent collisions. Convergence results for the algorithm are provided for functions which satisfy the Polyak-Łojasiewicz inequality. Simulations and numerical results are provided to support the theoretical results.

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Predictive online convex optimization

Cited by 23 publications

References 15 publications

Second-order Online Nonconvex Optimization

Second-order Online Nonconvex Optimization

Information Aggregation for Constrained Online Control

Optimization with Zeroth-Order Oracles in Formation

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