Gen-DFL: Decision-Focused Generative Learning for Robust Decision Making

TL;DR

Gen-DFL addresses uncertainty in high-dimensional, risk-sensitive decision problems by learning the conditional distribution $p(c|x)$ with conditional normalizing flows and optimizing tail-risk via CVaR. It pairs a generate-then-optimize paradigm with a joint loss that blends decision-focused regret and generative-model objectives, enabling adaptive sampling from high-risk regions without over-conservatism. Theoretical results bound the surrogate-regret gap via distributional distance and quantify improvement over traditional Pred-DFL, especially as problem dimensionality and tail risk increase. Empirically, Gen-DFL outperforms baselines on portfolio management, knapsack, shortest-path, and energy scheduling tasks, demonstrating enhanced robustness and decision quality in diverse settings.

Abstract

Decision-focused learning (DFL) integrates predictive models with downstream optimization, directly training machine learning models to minimize decision errors. While DFL has been shown to provide substantial advantages when compared to a counterpart that treats the predictive and prescriptive models separately, it has also been shown to struggle in high-dimensional and risk-sensitive settings, limiting its applicability in real-world settings. To address this limitation, this paper introduces decision-focused generative learning (Gen-DFL), a novel framework that leverages generative models to adaptively model uncertainty and improve decision quality. Instead of relying on fixed uncertainty sets, Gen-DFL learns a structured representation of the optimization parameters and samples from the tail regions of the learned distribution to enhance robustness against worst-case scenarios. This approach mitigates over-conservatism while capturing complex dependencies in the parameter space. The paper shows, theoretically, that Gen-DFL achieves improved worst-case performance bounds compared to traditional DFL. Empirically, it evaluates Gen-DFL on various scheduling and logistics problems, demonstrating its strong performance against existing DFL methods.

Figures (6)

• Figure 1: Comparison of the proposed decision-focused generative learning (Gen-DFL) framework with conventional predict-then-optimize (PTO) and decision-focused learning (DFL).
• Figure 2: Overview of the proposed Gen-DFL framework. The right panel compares Gen-DFL with the traditional DFL approaches which either relies a point predictor (Pred-DFL) or assume that the conditional distribution $p(c|x)$ follows a simpler form (an isotropic Gaussian) (Pred-DFL+). In contrast, Gen-DFL leverages a generative model to capture $p(c|x)$ while incorporating the decision-making objective which emphasizes the high-risk region.
• Figure 3: Comparison of decision quality in the portfolio task under different settings. We present box plots of the percentage regret ($\downarrow$ , lower is better), generated from 10 repeated experiments.
• Figure 4: Decision quality against different risk-sensitive regions vs various hyperparameters $\beta$.
• Figure 5: Decision quality evaluated w.r.t the risk levels for models trained by different $\alpha$.

Theorems & Definitions (22)

• Theorem 5.1
• proof
• Definition 5.2
• Definition 5.3
• Theorem 5.4
• Remark 5.5
• Remark 5.6
• proof
• Theorem 1.1
• proof