# OTSS: Output-Targeted Soft Segmentation for Contextual Decision-Weight Learning

arXiv: https://arxiv.org/abs/2605.00193 · HTML: https://mlsanity.com/paper/2605.00193/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 26 references that are in the map.
- First posted on arXiv 30 Apr 2026.

## Builds on (most cited first, 14 of 14)

- [Smart "Predict, then Optimize"](https://mlsanity.com/paper/1710.08005/) (2017)
- [Differentiation of Blackbox Combinatorial Solvers](https://mlsanity.com/paper/1912.02175/) (2019)
- [Decision-Focused Learning: Foundations, State of the Art, Benchmark and Future Opportunities](https://mlsanity.com/paper/2307.13565/) (2023)
- [Off-policy evaluation for slate recommendation](https://mlsanity.com/paper/1605.04812/) (2016)
- [A Survey of Contextual Optimization Methods for Decision Making under Uncertainty](https://mlsanity.com/paper/2306.10374/) (2023)
- [Open Bandit Dataset and Pipeline: Towards Realistic and Reproducible Off-Policy Evaluation](https://mlsanity.com/paper/2008.07146/) (2020)
- [Contextual Bandits with Latent Confounders: An NMF Approach](https://mlsanity.com/paper/1606.00119/) (2016)
- [Sigmoid Gating is More Sample Efficient than Softmax Gating in Mixture of Experts](https://mlsanity.com/paper/2405.13997/) (2024)
- [On Least Square Estimation in Softmax Gating Mixture of Experts](https://mlsanity.com/paper/2402.02952/) (2024)
- [Contextual Inverse Optimization: Offline and Online Learning](https://mlsanity.com/paper/2106.14015/) (2021)
- [Discovering Context Effects from Raw Choice Data](https://mlsanity.com/paper/1902.03266/) (2019)
- [Maximum Optimality Margin: A Unified Approach for Contextual Linear Programming and Inverse Linear Programming](https://mlsanity.com/paper/2301.11260/) (2023)
- [Inverse Contextual Bandits: Learning How Behavior Evolves over Time](https://mlsanity.com/paper/2107.06317/) (2021)
- [Mixtures of Experts Models](https://mlsanity.com/paper/1806.08200/) (2018)

## Abstract (arXiv)

Many machine learning systems make constrained decisions by optimizing factorized objectives, but the context-specific objective is often treated as fixed. We study contextual decision-weight learning: from logged decisions and proxy outputs, learn an optimizer-facing weight vector w(x) over interpretable decision factors z(x,d), rather than a direct policy or generic predictive score. We propose OTSS, an output-targeted soft-segmentation model that deploys the personalized decision-ready weight vector. At the function-class level, the theory highlights a hard-versus-soft distinction. Hard partitions incur an approximation-estimation tradeoff under overlap, while a realizable fixed-K soft class removes the hard-partition approximation floor and attains a parametric rate. We evaluate OTSS in controlled benchmarks with finite evaluation libraries, where the true weight vector and downstream regret can be computed exactly. In the representative overlap setting, OTSS attains the lowest mean regret among the comparators, including EM mixture regression, the strongest soft-mixture baseline in our comparison; it matches EM on coefficient recovery while running about two orders of magnitude faster. In a matched K=5 benchmark, OTSS remains competitive under hard-routed truth and improves as heterogeneity becomes softer and sample size grows. On a fixed Complete Journey retail anchor with real household covariates and action geometry, OTSS again achieves the lowest mean-regret point estimate.