Time-Varying Optimization for Streaming Data Via Temporal Weighting

• URL: http://arxiv.org/abs/2510.13052v1
• Date: Wed, 15 Oct 2025 00:18:17 GMT
• Title: Time-Varying Optimization for Streaming Data Via Temporal Weighting
• Authors: Muhammad Faraz Ul Abrar, Nicolò Michelusi, Erik G. Larsson,
• Abstract summary: We study the problem of learning from streaming data through a time-varying optimization lens.<n>We focus on two specific weighting strategies: (1) uniform weights, which treat all samples equally, and (2) discounted weights, which geometrically decay the influence of older data.<n>Our theoretical findings are validated through numerical simulations.
• Score: 26.702871313273942
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Classical optimization theory deals with fixed, time-invariant objective functions. However, time-varying optimization has emerged as an important subject for decision-making in dynamic environments. In this work, we study the problem of learning from streaming data through a time-varying optimization lens. Unlike prior works that focus on generic formulations, we introduce a structured, \emph{weight-based} formulation that explicitly captures the streaming-data origin of the time-varying objective, where at each time step, an agent aims to minimize a weighted average loss over all the past data samples. We focus on two specific weighting strategies: (1) uniform weights, which treat all samples equally, and (2) discounted weights, which geometrically decay the influence of older data. For both schemes, we derive tight bounds on the ``tracking error'' (TE), defined as the deviation between the model parameter and the time-varying optimum at a given time step, under gradient descent (GD) updates. We show that under uniform weighting, the TE vanishes asymptotically with a $\mathcal{O}(1/t)$ decay rate, whereas discounted weighting incurs a nonzero error floor controlled by the discount factor and the number of gradient updates performed at each time step. Our theoretical findings are validated through numerical simulations.

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