# Time-Varying Optimization for Streaming Data Via Temporal Weighting

arXiv: https://arxiv.org/abs/2510.13052 · HTML: https://mlsanity.com/paper/2510.13052/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 19 references that are in the map.
- First posted on arXiv 15 Oct 2025.

## Builds on (most cited first, 12 of 12)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (2016)
- [Continual Lifelong Learning with Neural Networks: A Review](https://mlsanity.com/paper/1802.07569/) (2018)
- [A Comprehensive Survey of Continual Learning: Theory, Method and Application](https://mlsanity.com/paper/2302.00487/) (2023)
- [Time-Varying Convex Optimization: Time-Structured Algorithms and Applications](https://mlsanity.com/paper/2006.08500/) (2020)
- [A Class of Prediction-Correction Methods for Time-Varying Convex Optimization](https://mlsanity.com/paper/1509.05196/) (2015)
- [Optimization and Learning with Information Streams: Time-varying Algorithms and Applications](https://mlsanity.com/paper/1910.08123/) (2019)
- [Unified Analysis of Decentralized Gradient Descent: a Contraction Mapping Framework](https://mlsanity.com/paper/2503.14353/) (2025)
- [Distributed Convex Optimization for Continuous-Time Dynamics with Time-Varying Cost Function](https://mlsanity.com/paper/1507.04878/) (2015)
- [Dynamic Filtering of Time-Varying Sparse Signals via l1 Minimization](https://mlsanity.com/paper/1507.06145/) (2015)
- [Energy-Efficient Federated Edge Learning with Streaming Data: A Lyapunov Optimization Approach](https://mlsanity.com/paper/2405.12046/) (2024)
- [Decentralized Prediction-Correction Methods for Networked Time-Varying Convex Optimization](https://mlsanity.com/paper/1602.01716/) (2016)

## Built on by (most cited first, 2 of 2)

- [Decentralized Time-Varying Optimization for Streaming Data via Temporal Weighting](https://mlsanity.com/paper/2605.06971/) (2026)
- [Distributed Optimization with Streaming Data: A Temporal Weighting Perspective](https://mlsanity.com/paper/2608.09565/) (2026)

## Abstract (arXiv)

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, 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 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.