{"ID":2854920,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.13052","arxiv_id":"2510.13052","title":"Time-Varying Optimization for Streaming Data Via Temporal Weighting","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.","short_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 prio...","url_abs":"https://arxiv.org/abs/2510.13052","url_pdf":"https://arxiv.org/pdf/2510.13052v1","authors":"[\"Muhammad Faraz Ul Abrar\",\"Nicolò Michelusi\",\"Erik G. Larsson\"]","published":"2025-10-15T00:18:17Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.AI\",\"eess.SP\",\"eess.SY\",\"math.OC\"]","methods":"[]","has_code":false}