# Online Decision-Focused Learning

arXiv: https://arxiv.org/abs/2505.13564 · HTML: https://mlsanity.com/paper/2505.13564/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 45 of its 90 references that are in the map.
- First posted on arXiv 19 May 2025.

## Builds on (most cited first, 30 of 45)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programming](https://mlsanity.com/paper/1309.5549/) (2013)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Learning under Concept Drift: A Review](https://mlsanity.com/paper/2004.05785/) (2020)
- [Smart "Predict, then Optimize"](https://mlsanity.com/paper/1710.08005/) (2017)
- [Melding the Data-Decisions Pipeline: Decision-Focused Learning for Combinatorial Optimization](https://mlsanity.com/paper/1809.05504/) (2018)
- [Bilevel Optimization: Convergence Analysis and Enhanced Design](https://mlsanity.com/paper/2010.07962/) (2020)
- [Non-stationary Stochastic Optimization](https://mlsanity.com/paper/1307.5449/) (2013)
- [Fast Convergence of Regularized Learning in Games](https://mlsanity.com/paper/1507.00407/) (2015)
- [From Predictive to Prescriptive Analytics](https://mlsanity.com/paper/1402.5481/) (2014)
- [Adaptive Online Learning in Dynamic Environments](https://mlsanity.com/paper/1810.10815/) (2018)
- [Decision-Focused Learning: Foundations, State of the Art, Benchmark and Future Opportunities](https://mlsanity.com/paper/2307.13565/) (2023)
- [A Review on Bilevel Optimization: From Classical to Evolutionary Approaches and Applications](https://mlsanity.com/paper/1705.06270/) (2017)
- [On Differentiating Parameterized Argmin and Argmax Problems with Application to Bi-level Optimization](https://mlsanity.com/paper/1607.05447/) (2016)
- [Dynamic Regret of Convex and Smooth Functions](https://mlsanity.com/paper/2007.03479/) (2020)
- [Learning to Optimize under Non-Stationarity](https://mlsanity.com/paper/1810.03024/) (2018)
- [Interior Point Solving for LP-based prediction+optimisation](https://mlsanity.com/paper/2010.13943/) (2020)
- [A Survey of Contextual Optimization Methods for Decision Making under Uncertainty](https://mlsanity.com/paper/2306.10374/) (2023)
- [On the Almost Sure Convergence of Stochastic Gradient Descent in Non-Convex Problems](https://mlsanity.com/paper/2006.11144/) (2020)
- [Decision-Focused Learning: Through the Lens of Learning to Rank](https://mlsanity.com/paper/2112.03609/) (2021)
- [A Faster Interior Point Method for Semidefinite Programming](https://mlsanity.com/paper/2009.10217/) (2020)
- [Optimal Stochastic Non-smooth Non-convex Optimization through Online-to-Non-convex Conversion](https://mlsanity.com/paper/2302.03775/) (2023)
- [Dynamical Models and Tracking Regret in Online Convex Programming](https://mlsanity.com/paper/1301.1254/) (2013)
- [Improved Analysis for Dynamic Regret of Strongly Convex and Smooth Functions](https://mlsanity.com/paper/2006.05876/) (2020)
- [Online Non-Convex Learning: Following the Perturbed Leader is Optimal](https://mlsanity.com/paper/1903.08110/) (2019)
- [Efficient Regret Minimization in Non-Convex Games](https://mlsanity.com/paper/1708.00075/) (2017)
- [Online Linear Optimization via Smoothing](https://mlsanity.com/paper/1405.6076/) (2014)
- [Learning in Non-convex Games with an Optimization Oracle](https://mlsanity.com/paper/1810.07362/) (2018)
- [Online Learning with Inexact Proximal Online Gradient Descent Algorithms](https://mlsanity.com/paper/1806.00202/) (2018)

## Built on by (most cited first, 4 of 4)

- [Combinatorial Optimization Augmented Machine Learning](https://mlsanity.com/paper/2601.10583/) (2026)
- [Decision-Focused On-Policy Learning for Contextual Linear Optimization with Partial Feedback](https://mlsanity.com/paper/2606.01081/) (2026)
- [Decision-Focused Learning: When and Why Traditional Prediction Models Fail](https://mlsanity.com/paper/2606.21773/) (2026)
- [IGT-OMD: Implicit Gradient Transport for Decision-Focused Learning under Delayed Feedback](https://mlsanity.com/paper/2605.12693/) (2026)

## Abstract (arXiv)

Decision-focused learning (DFL) is an increasingly popular paradigm for training predictive models whose outputs are used in decision-making tasks. Instead of merely optimizing for predictive accuracy, DFL trains models to directly minimize the loss associated with downstream decisions. However, existing studies focus solely on scenarios where a fixed batch of data is available and the objective function does not change over time. We instead investigate DFL in dynamic environments where the objective function and data distribution evolve over time. This setting is challenging for online learning because the objective function has zero or undefined gradients, which prevents the use of standard first-order optimization methods, and is generally non-convex. To address these difficulties, we (i) regularize the objective to make it differentiable and (ii) use perturbation techniques along with a near-optimal oracle to overcome non-convexity. Combining those techniques yields two original online algorithms tailored for DFL, for which we establish respectively static and dynamic regret bounds. These are the first provable guarantees for the online decision-focused problem. Finally, we showcase the effectiveness of our algorithms on a knapsack experiment, where they outperform two standard benchmarks.