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FedRSPO+: A Heterogeneity-aware Algorithm for Decision-focused Federated Learning

NeurIPS 2026 · Federated learning and privacy › Personalized and heterogeneous FL · approach: Non-IID federated learning

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Proposes FedRSPO+, a federated decision-focused learning method built on RSPO+, a Moreau-envelope-smoothed SPO+ surrogate whose projection-based decisions are stable under objective and feasible-set heterogeneity, with annealed regularization and per-client calibration.

Problem

Decision-focused learning in cross-silo federated settings where clients have heterogeneous objectives and polyhedral feasible sets; SPO+ optimal decisions are discontinuous under such heterogeneity, making federated aggregation unstable.

Approach

Replace the discontinuous LP solution map in SPO+ with a Moreau-envelope-smoothed surrogate (RSPO+) whose decision is a Euclidean projection onto the feasible set, and anneal the regularization parameter lambda toward the original LP with a freezing rule, combined with federated warm-start and personalization.

Key results

• On the synthetic knapsack with no heterogeneity, RSPO+ federated reaches 2.3% relative regret vs 9.7% for SPO+ (after personalization 1.9% vs 5.6%).
• On PJM, the full FedRSPO+ achieves 60.7 mean absolute regret ($), versus 81.7 for SPO+ federation and 175.5 for MSE.
• On Warcraft shortest path, FedRSPO+ reaches 2.571% optimality gap after personalization, losing marginally to SPO+ (1.850%).

Surprising findings

• Warcraft shortest path: the quadratic regularization breaks total unimodularity, so FedRSPO+ underperforms SPO+ there, a stated limitation.
• Ditto personalization conflicts with the annealing schedule and performs similarly to RSPO+ with personalization on PJM.

Limitations

• Regret guarantees hold for the regularized decision and apply to LP decisions only under exact regularization, which the stopping rule does not enforce.
• Convergence analysis covers linear predictors while main experiments use neural networks.
• Convexity assumptions exclude mixed-integer programs; method is less effective when downstream structure is incompatible with quadratic regularization (e.g., shortest path).

Experimental setup

Datasets: synthetic fractional knapsack PJM day-ahead electricity prices 2025 Open-Meteo weather data Warcraft shortest path 12x12

Benchmarks: synthetic fractional knapsack PJM case study Warcraft shortest path

Metrics: relative regret (%) mean absolute regret ($) optimality gap (%)

Baselines: MSE SPO+ PFYL DPO Interp-DFFL OptNet-style QP FedProx Ditto

Builds on: SPO+ Interp-DFFL FedProx Ditto perturbed Fenchel-Young loss

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