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Integrating Inference and Experimental Design for Contextual Behavioral Model Learning
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Proposes sequential experimental design methods (inference-then-design with learnable priors and an integrated inference-and-design objective) to collect informative choice data for learning contextual behavioral models of investors in portfolio choice.
Problem
Learning how users' hidden information (risk aversion, decision rationality) depends on observable context from behavioral choice data, where the platform must actively design sequential experiments to collect the most informative data.
Approach
Infer a variational posterior over neural network weights and choose designs by expected information gain; improve it by setting the prior from a maximum-likelihood fit on historical data (ID-LP) and by deriving a joint lower bound that couples variational inference with the design step (I-ID-LP), adding a KL-based term to the inference objective.
Key results
- I-ID-LP achieves the lowest NLL in settings A, B, C, D (e.g., 0.408 vs 0.416 for ID in setting A; 0.297 vs 0.319 in setting B) across 20 seeds.
- Baselines such as MinMaxPro and PreEntropy have NLL above 0.55 in setting A and far higher variance than the proposed methods.
- ID-LP runs fastest (about 426 s per seed) versus 2522 s for ID and 3721 s for I-ID-LP over 15 periods.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use a learnable prior instead of a randomly chosen prior (ablation) | ID · Setting A | NLL loss: 0.416 -> 0.409 | Helped |
| Use a learnable prior instead of a randomly chosen prior (ablation) | ID · Setting B | NLL loss: 0.319 -> 0.306 | Helped |
| Use a learnable prior instead of a randomly chosen prior (ablation) | ID · Setting C | NLL loss: 0.397 -> 0.390 | Helped |
| Use a learnable prior instead of a randomly chosen prior (ablation) | ID · Setting D | NLL loss: 0.381 -> 0.376 | Helped |
| Use a learnable prior instead of a randomly chosen prior (ablation) | ID · Setting E | NLL loss: 0.391 -> 0.383 | Helped |
| Integrate inference and design rather than optimizing them separately (ablation) | ID-LP · Setting A | NLL loss: 0.409 -> 0.408 | Helped |
| Integrate inference and design rather than optimizing them separately (ablation) | ID-LP · Setting B | NLL loss: 0.306 -> 0.297 | Helped |
| Integrate inference and design rather than optimizing them separately (ablation) | ID-LP · Setting C | NLL loss: 0.390 -> 0.387 | Helped |
| Integrate inference and design rather than optimizing them separately (ablation) | ID-LP · Setting D | NLL loss: 0.376 -> 0.369 | Helped |
| Integrate inference and design rather than optimizing them separately (ablation) | ID-LP · Setting E | NLL loss: 0.383 -> 0.383 | No clear effect |
Surprising findings
- Choosing the design with the lowest EIG (ID-LP-minEIG) performs worst, showing strong sensitivity of data quality to design EIG.
- Random prior for ID disrupts early-period inference, motivating a data-driven prior; the gain of I-ID-LP over ID-LP is small in some settings (e.g., setting A 0.408 vs 0.409).
Limitations
- Assumes the logit portfolio choice model is known and only the context-to-hidden-information mapping is unknown.
- Experiments are on simulated data with unknown but fixed arrival dynamics; does not consider future investor arrivals.
- Evaluation uses predictive NLL rather than downstream performance such as portfolio profit.
Experimental setup
Datasets: synthetic simulated investor choice data (16-dim contexts, 10 designs, K=2 portfolios)
Benchmarks: simulated portfolio choice settings A-E
Metrics: negative log-likelihood loss on test set MSE of predicted r(x) and lambda(x)
Baselines: ID ID-LP-minEIG ID-LP-medEIG PreEntropy MinMaxPro LaplaceInfer Random MaxMean
Builds on: Bayesian optimal experimental design (EIG with nested Monte Carlo) mean-field variational inference Bayesian neural networks (Blundell et al. 2015) Markowitz mean-variance model logit choice model
Closest papers by meaning
- Distributional Preference Learning: Understanding and Accounting for Hidden Context in RLHF (ICLR 2024 · similarity 0.85)
- BehaviorBench: Modeling Real-World User Decisions from Behavioral Traces (NeurIPS 2026 · similarity 0.84)
- MultiScale Contextual Bandits for Long Term Objectives (NeurIPS 2025 · similarity 0.84)
- Cost-Aware Near-Optimal Policy Learning (AAAI 2025 · similarity 0.84)
- A Parametric Contextual Online Learning Theory of Brokerage (ICML 2025 · similarity 0.84)
- Can In-Context Learning Support Intrinsic Curiosity? (NeurIPS 2026 · similarity 0.84)
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