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Inverse decision-making using neural amortized Bayesian actors
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Amortizes the Bayesian actor's optimal action with a neural network trained unsupervised on the expected cost, then uses it inside NUTS-based gradient inference of actor parameters and priors/costs from continuous sensorimotor behavior.
Problem
Inverse decision-making for Bayesian actor models with continuous actions is intractable when the expected cost lacks closed-form solutions (non-quadratic costs, non-Gaussian noise), so inferring priors, uncertainties, and costs from behavior is computationally prohibitive.
Approach
Train an MLP to approximate the optimal Bayesian action directly by minimizing the expected posterior loss of the decision problem (unsupervised, no numerically solved actions), then plug the differentiable network into a probabilistic model so gradient-based HMC (NUTS) can infer parameters from behavioral data.
Key results
- For the quadratic cost, NN-based posterior MSE matched the analytical version (e.g., mu0 MSE 0.10 vs 0.10; sigma0 3.98e-4 vs 3.77e-4).
- Inference of a 60-trial dataset with 20,000 posterior samples took about 10 seconds; training 500,000 steps took about 10 minutes.
- Varying perceptual uncertainty across two levels (sigma in {0.1, 0.2}) disentangled prior mean mu0 and effort cost beta in simulation, whereas a single level left them correlated and less precise.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use neural-network optimal actions instead of analytical optimal actions | Bayesian parameter inference with quadratic cost · Synthetic quadratic cost | MSE, μ₀: 0.10 -> 0.10 | No clear effect |
| Use neural-network optimal actions instead of analytical optimal actions | Bayesian parameter inference with quadratic cost · Synthetic quadratic cost | MSE, σ₀: $3.98 \times 10^{-4}$ -> $3.77 \times 10^{-4}$ | Helped |
| Use neural-network optimal actions instead of analytical optimal actions | Bayesian parameter inference with quadratic cost · Synthetic quadratic cost | MSE, σᵣ: $6.23 \times 10^{-4}$ -> $6.13 \times 10^{-4}$ | Helped |
| Use neural-network optimal actions instead of analytical optimal actions | Bayesian parameter inference with quadratic cost and quadratic effort · Synthetic quadratic cost with quadratic effort | MSE, μ₀: 0.74 -> 0.77 | Hurt |
| Use neural-network optimal actions instead of analytical optimal actions | Bayesian parameter inference with quadratic cost and quadratic effort · Synthetic quadratic cost with quadratic effort | MSE, β: $8.97 \times 10^{-4}$ -> $8.97 \times 10^{-3}$ | Hurt |
| Fix one of the confounding parameters at its true value instead of inferring both (ablation) | Asymmetric quadratic cost inference · Synthetic asymmetric quadratic cost | MSE of inferred parameters | Helped |
| Use two levels of perceptual uncertainty rather than one level | Quadratic cost with quadratic effort inference · Simulated experiment with two perceptual uncertainty conditions | Posterior uncertainty in μ₀ and β | Helped |
| Use one level of perceptual uncertainty rather than two levels (ablation) | Quadratic cost with quadratic effort inference · Simulated experiment with one perceptual uncertainty condition | Posterior uncertainty in μ₀ and β | Hurt |
| Fix one of sensory uncertainty σ or prior uncertainty σ₀ at its true value (ablation) | Bayesian actor parameter inference · Synthetic Bayesian actor data | MSE of inferred confounding parameter | Helped |
| Use the Linex cost function rather than the best-fitting cost function | Bayesian actor model fitted to force reproduction data · Force reproduction (FOR) | Model fit | Hurt |
| Use asymmetric cost rather than other evaluated costs | Bayesian actor model fitted to bean bag throwing data · Bean bag throwing (BB) | Model fit | Helped |
| Compare different cost functions on puck sliding data | Bayesian actor model fitted to puck sliding data · Puck sliding (PU) | Model comparison | No clear effect |
Surprising findings
- Prior mean and asymmetric cost parameter (and prior and effort cost) are confounded, so undershoots can be explained equally by a biased prior or a cost, making them non-identifiable in a single-condition experiment.
- Sigma and sigma0 are jointly unidentifiable; only their ratio is constrained by behavior.
Limitations
- Requires a perceptual model that allows sampling from the observer's posterior (log-normal case used), so circular or non-magnitude stimuli are not covered.
- Inference relies on priors restricted to the range the network was trained on, and perceptual uncertainty sigma had to be fixed to avoid identifiability issues.
Experimental setup
Datasets: synthetic data from Bayesian actor model bean bag throwing data (Willey and Liu) puck sliding data force reproduction data (Onneweer)
Benchmarks: synthetic parameter recovery (100 simulated datasets) bean bag throwing puck sliding force reproduction
Metrics: mean squared error between posterior mean and ground truth R-hat PSIS-LOO ELPD posterior predictive checks
Baselines: analytical posterior (quadratic cost) numerically solved optimal actions
Builds on: inverse optimal control doubly-Bayesian analysis NUTS swish activation
Closest papers by meaning
- Inverse Optimal Control Adapted to the Noise Characteristics of the Human Sensorimotor System (NeurIPS 2021 · similarity 0.88)
- Probabilistic inverse optimal control for non-linear partially observable systems disentangles perceptual uncertainty and behavioral costs (NeurIPS 2023 · similarity 0.88)
- An Information-Theoretical Framework For Optimizing Experimental Design To Distinguish Probabilistic Neural Codes (ICLR 2026 · similarity 0.88)
- A sampling-based circuit for optimal decision making (NeurIPS 2021 · similarity 0.87)
- Act to See, See to Act: Diffusion-Driven Perception-Action Interplay for Adaptive Policies (NeurIPS 2025 · similarity 0.85)
- Model–Behavior Alignment under Flexible Evaluation: When the Best-Fitting Model Isn’t the Right One (NeurIPS 2025 · similarity 0.85)
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