Konstantinos Ziliaskopoulos

Konstantinos Ziliaskopoulos, Alexander Vinel

We consider what we refer to as {Decision-Focused Federated Learning (DFFL)} framework, i.e., a predict-then-optimize approach employed by a collection of agents, where each agent's predictive model is an input to a downstream linear optimization problem, and no direct exchange of raw data is allowed. Importantly, clients can differ both in objective functions and in feasibility constraints. We build on the well-known SPO+ approach and develop heterogeneity bounds for the SPO+ surrogate loss in this case. This is accomplished by employing a support function representation of the feasible region, separating (i) objective shift via norm distances between the cost vectors and (ii) feasible-set shift via shape distances between the constraint sets. In the case of strongly convex feasible regions, sharper bounds are derived due to the optimizer stability. Building on these results, we define a heuristic local-versus-federated excess risk decision rule which, under SPO+ risk, gives a condition for when federation can be expected to improve decision quality: the heterogeneity penalty must be smaller than the statistical advantage of pooling data. We implement a FedAvg-style DFFL set of experiments on both polyhedral and strongly convex problems and show that federation is broadly robust in the strongly convex setting, while performance in the polyhedral setting degrades primarily with constraint heterogeneity, especially for clients with many samples. In other words, especially for the strongly convex case, an approach following a direct implementation of FedAvg and SPO+ can still yield promising performance even when the downstream optimization problems are noticeably different.

Konstantinos Ziliaskopoulos, Alexander Vinel, Alice E. Smith

Predictive models are increasingly embedded in operational decision-making, yet standard explanation methods typically explain forecasts rather than the decisions those forecasts induce. This distinction is important in predict-then-optimize systems: large forecast changes may leave the optimizer's action unchanged, while small changes can alter the selected decision and its realized value. We propose Decision Value Attribution (DVA), a Shapley-based framework for attributing the value of a fixed prediction--optimization pipeline. The framework defines cooperative games whose payoff is the downstream decision value, allowing the players to be information sources, optimization or design parameters, or both. We present three variants: InfoDVA attributes value to features, DesignDVA attributes value to operational configurations, and Decision-Value Interactions (DVI) quantifies how information and design jointly create value. We further distinguish post-DVA, which evaluates decisions using realized outcomes, from pre-DVA, which evaluates decisions under the model's full prediction. This separation turns attribution into a decision-level diagnostic of whether the model's operational beliefs align with realized performance. The resulting attributions are expressed in the units of the operational objective and decompose the gain or loss relative to a baseline. Case studies in electricity storage arbitrage and emergency medical service coverage show that predictive explanations can be poor proxies for operational value, that DVA can guide targeted information-control interventions, and that optimization configurations determine when predictive information is decision-relevant.