Modelling Task 2: Bayesian Policy Inference Simulation

Project: corpora-task-modelling-1778795810213-620a9917 • Generated: 2026-05-14 22:57

Hierarchical Bayesian inference with variational Monte Carlo to quantify policy uncertainty under noisy observations before deployment.

Bayesian InferenceMonte CarloVariational InferenceFeasibilitydepends on #1: Synthetic Adversarial Observation Perturbation Dataset Generation

Source in Roadmap / Ideate	Chapter 1 – AOI-GBE Model Development
Why model first	Enables quantitative assessment of policy uncertainty and robustness to unseen perturbations, guiding architecture choices without requiring live agent deployment.

What Is Modelled

The posterior distribution over agent policy parameters given a stream of noisy observations, where observations are corrupted by adversarial perturbations or sensor noise. The model captures the joint distribution of clean and perturbed observations using a conditional generative model and marginalises over it to obtain a calibrated policy posterior.

Objectives

Build a hierarchical Bayesian model that jointly learns a conditional generative observation model (CC‑GAN) and a policy prior.
Implement variational Monte Carlo (VMC) and Hamiltonian Monte Carlo (HMC) inference engines to sample from the policy posterior.
Quantify calibration (ECE, Brier score) and robustness (policy regret under unseen perturbations) of the posterior.
Provide a hyper‑heuristic orchestrator that selects the best inference engine and hyper‑parameters within a compute budget.
Generate synthetic observation logs for validation and stress‑testing.

Success Criteria

Posterior predictive checks show <5% calibration error on held‑out perturbed data.
Policy regret under 30% unseen perturbations is <10% relative to nominal policy.
Hyper‑heuristic converges to the best inference engine within 200 evaluations.
Synthetic data generation reproduces the statistical properties of real logs (KL divergence <0.1).

Output Form

A Python package exposing a `PolicyPosteriorSampler` API that returns posterior samples, calibration metrics, and a provenance log. Includes a Jupyter notebook demo and a Docker image for reproducibility.

Key Parameters & What They Affect

Parameter	Range / Units	Affects	Notes
observation_noise_std	0.0 – 1.0 (Gaussian std)	calibrationpolicy uncertainty	Higher values increase posterior entropy and test robustness.
policy_prior_variance	0.1 – 10.0	posterior concentrationbias–variance trade‑off	Controls how strongly the prior influences the posterior.
num_variational_samples	50 – 500	estimation variancecompute time	Trade‑off between Monte Carlo noise and runtime.
hmc_steps	10 – 100	mixing speedsampling cost	Number of leapfrog steps per HMC trajectory.

Input Data

Required data:

clean observation sequences (sensor streams)
corrupted observation sequences (adversarial / noisy)
policy execution traces (state, action, reward)
policy network architecture definition

Natural Sources (from the project)

Chapter 1 – AOI‑GBE test‑rig logs (sensor data, perturbation metadata)
Supplier data on UAV sensor noise profiles (from Chapter 1 roadmap)
Prior policy network outputs from the simulation environment (Chapter 1 prototype)

Acquired Sources

OpenAI Gym / MuJoCo environments for baseline policy training
CARLA autonomous driving simulator for realistic sensor streams
Open datasets of adversarial perturbations (e.g., Adversarial Patch dataset)
Stan or PyMC3 model templates from the literature

Synthesised Sources

Conditional GAN (CC‑GAN) trained on clean/corrupted pairs to generate synthetic perturbed observations.
Physics‑based noise injection scripts (e.g., adding Gaussian, salt‑pepper, or semantic perturbations).

Engineer / Scientist Guidance

Define the observation generative model as a conditional GAN (CC‑GAN) using PyTorch; condition on available sensor context and a latent noise vector.
Implement the hierarchical Bayesian policy model in Pyro: plates for observations, policy parameters, and hyper‑parameters.
Set up two inference back‑ends: (a) stochastic variational inference (SVI) with black‑box ELBO; (b) Hamiltonian Monte Carlo (HMC) via NumPyro’s NUTS.
Create a hyper‑heuristic orchestrator using Optuna: each trial proposes a tuple (inference_engine, num_samples, hmc_steps, lr, prior_variance).
Define the evaluation metric as a weighted sum of Expected Calibration Error (ECE) and policy regret on a held‑out perturbation set.
Use a multi‑armed bandit (Thompson sampling) to select inference engines; update posterior over engine performance after each trial.
Implement synthetic data generation: sample latent vectors, generate clean and perturbed observations via CC‑GAN, and store in HDF5 for reproducibility.
Wrap the entire workflow in a Docker container; expose a REST API that accepts observation batches and returns posterior samples and metrics.
Document the provenance of each sample (model version, hyper‑parameters, synthetic seed) in a JSON log for auditability.
Validate the posterior by running posterior predictive checks: generate synthetic trajectories and compare with real ones using KS‑test and Wasserstein distance.

Recommended Tools

Pyro (for probabilistic programming)NumPyro (for GPU‑accelerated HMC)Optuna (hyper‑parameter optimization & bandit)TensorFlow Probability (alternative VI)PyTorch (for CC‑GAN implementation)HDF5 / Zarr (data storage)Docker (containerization)JupyterLab (interactive notebooks)Prometheus + Grafana (runtime monitoring)GitHub Actions (CI/CD for model training)

Validation & Verification

Posterior predictive checks will be performed on a held‑out set of perturbed observations. Calibration will be measured using Expected Calibration Error (ECE) and Brier score. Policy robustness will be quantified by computing regret against a nominal policy under a separate set of unseen perturbations. Results will be benchmarked against a baseline deterministic policy and an oracle that has access to clean observations.

Expected Impact

Quality

Provides a statistically sound estimate of policy uncertainty, reducing over‑confidence in deployment.

Timescale

Enables rapid pre‑deployment validation (≈2–3 weeks) instead of full field trials.

Cost

Avoids costly on‑the‑fly retraining by identifying robust policies early; estimated savings of 20–30% in compute spend.

Risk Retired

Mitigates risk of catastrophic failure due to unseen observation perturbations and improves regulatory auditability.

Software Tool Development Prompts

Drop these into a coding assistant toscaffold the supporting software for this modelling task.

Create a Python class `PolicyPosteriorSampler` that uses Pyro to define a hierarchical Bayesian model with a conditional GAN observation model and a policy prior. The class should expose a `sample_posterior(observations, num_samples)` method that returns posterior samples and a `evaluate_calibration(samples, true_actions)` method that computes ECE and Brier score.

Implement an Optuna study that optimizes over inference engines (SVI, HMC), number of variational samples, HMC steps, learning rate, and prior variance. Use a custom objective that returns the weighted sum of calibration error and policy regret. Include a multi‑armed bandit callback that records the best performing engine and stops the study after 200 trials or when improvement < 1e-3.

Write a Dockerfile that installs Pyro, NumPyro, Optuna, and PyTorch, copies the `PolicyPosteriorSampler` code, and exposes a Flask API endpoint `/sample` that accepts JSON observations and returns posterior samples and metrics.

Risks & Assumptions

Assumes Gaussian observation noise; non‑Gaussian or adversarial noise may degrade model performance.
Assumes the policy parameter space is continuous and can be represented by a neural network; discrete action spaces require additional modeling.
Variational inference may under‑estimate posterior variance; HMC may be computationally expensive for high‑dimensional policies.
Synthetic data generation relies on the CC‑GAN’s ability to capture the true joint distribution; mode collapse could bias the posterior.
Hyper‑heuristic selection may converge to a local optimum if the evaluation metric is noisy; robust stopping criteria are required.