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Contextual Optimization Under Model Misspecification: A Tractable and Generalizable Approach
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Proposes CILO, a surrogate loss for contextual optimization under model misspecification that is consistent with the true decision loss, with generalization bounds and a DC/Moreau-envelope smoothing procedure for tractable optimization.
Problem
Predict-then-optimize with a misspecified hypothesis class: standard SLO and SPO+ surrogates can select suboptimal cost predictors for the true decision loss.
Approach
A decision-aware surrogate (CILO) that subtracts the best achievable cost within a budget beta from the predicted-decision cost; it matches the optimal solutions of the true decision loss for suitable beta, is a difference of convex functions, and is smoothed via Moreau envelopes so gradient descent finds global minima for linear hypothesis classes.
Key results
- In well-specified settings SLO performs best; as misspecification grows, the proposed CILO approach outperforms SLO and SPO+ in regret across 96 runs per setting (synthetic linear hypothesis class).
- Theorem 1 shows minimizers of CILO loss coincide with minimizers of the true decision loss when beta equals the optimal budget and the hypothesis class is decision-well-specified.
- Theorem 4 shows that for linear hypothesis sets every stationary point of the smoothed surrogate is a global minimum.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use CILO instead of SLO | Contextual optimization under model misspecification · Synthetic data (s > 5; misspecified) | regret | Helped |
| use CILO instead of SPO+ | Contextual optimization under model misspecification · Synthetic data (s > 5; misspecified) | regret | Helped |
| use SLO instead of CILO | Contextual optimization · Synthetic data (s = 5; well-specified) | regret | Helped |
| increase the misspecification level | CILO, SLO, and SPO+ · Synthetic data (s > 5; misspecified) | regret | Mixed |
Surprising findings
- SLO, which is best under well-specification, performs worst under strong misspecification.
Limitations
- Experiments only on synthetic data; real-world validation planned but not done.
- Global optimality guarantee proven for linear hypothesis sets only.
- Requires line search over beta, and avoiding the zero solution needs additional log-barrier handling.
Experimental setup
Datasets: synthetic data
Benchmarks: synthetic contextual optimization experiments
Metrics: regret
Baselines: SPO+ SLO
Builds on: SPO+ sequential learning and optimization Moreau envelope smoothing
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