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

arXiv cs.LG / 5/4/2026

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Key Points

The paper studies contextual decision-weight learning, aiming to learn an optimizer-facing weight vector w(x) over interpretable decision factors rather than a fixed objective or a generic predictive score.
It introduces OTSS (Output-Targeted Soft Segmentation), a model that produces personalized, decision-ready soft segmentation of decision factors using theory about hard-versus-soft partitioning.
The theoretical results show that hard partitions can suffer an approximation-estimation tradeoff when partitions overlap, while a realizable fixed-K soft class avoids an approximation floor and achieves a parametric learning rate.
In controlled benchmarks where true weights and downstream regret can be computed exactly, OTSS achieves the lowest mean regret versus several comparators and can match EM on coefficient recovery while being about two orders of magnitude faster.
Across additional benchmarks, including a matched K=5 setting and a real retail “Complete Journey” anchor task, OTSS remains competitive and delivers the lowest mean-regret point estimates in the reported experiments.

Abstract

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.