# Feel-Good Thompson Sampling for Contextual Bandits: a Markov Chain Monte Carlo Showdown
This repository implements various MCMC-based contextual bandit algorithms.
## Features
- **Algorithms**:
- Langevin Monte Carlo (LMC)
- Underdamped Langevin Monte Carlo (ULMC)
- Metropolis-Adjusted Langevin Algorithm (MALA)
- Hamiltonian Monte Carlo (HMC)
- Epsilon-Greedy
- Upper-Confidence-Bound (UCB)
- Neural Thompson Sampling (NTS)
- Linear Thompson Sampling (LTS)
- Neural Upper-Confidence-Bound (NUCB)
- Neural Greedy (NG)
- And numerous variants with Feel-Good and smoothed Feel-Good exploration terms
- **Environments**:
- Linear bandits
- Logistic bandits
- Wheel bandit problem
- Neural bandits
## Installation
### Option 1: Install from PyPI (Recommended)
```bash
pip install ctx-bandits-mcmc
```
With optional dependencies:
```bash
# For development tools
pip install ctx-bandits-mcmc[dev]
# For neural bandit experiments
pip install ctx-bandits-mcmc[neural]
# All optional dependencies
pip install ctx-bandits-mcmc[dev,neural]
```
### Option 2: Install from Source
```bash
# Clone the repository
git clone https://github.com/SarahLiaw/ctx-bandits-mcmc-showdown.git
cd ctx-bandits-mcmc-showdown
# Install the package
pip install .
# Or install in editable mode for development
pip install -e .[dev]
```
### Option 3: Install from GitHub
```bash
pip install git+https://github.com/SarahLiaw/ctx-bandits-mcmc-showdown.git
```
For detailed installation instructions, platform-specific notes, and troubleshooting, see [INSTALL.md](INSTALL.md).
## Quick Start
### Running Linear Bandit Experiments
To run a linear bandit experiment with the LMC-TS agent:
```bash
python3 run.py --config_path config/linear/lmcts.json
```
### Running Wheel Bandit Experiments
To run the wheel bandit experiment with the ULMC agent:
```bash
python3 run_all_wheel_agents.py --agents ulmc --num_trials 1
```
### Batch Running Multiple Experiments
To run multiple experiments with different seeds:
```bash
python3 run_linear_batch.py --n_seeds 5
```
## Configuration
Configuration files are stored in the `config/` directory, organized by environment type (linear, logistic, wheel, neural). Each agent has its own configuration file with hyperparameters.
## Results
Results are saved in the `results/` directory by default. The directory structure is:
```
results/
├── linear/
├── logistic/
└── wheel/
└── neural/
```
## Posterior Distribution Quality Analysis
### Overview
The `posterior_analysis.py` script provides a controlled comparison of MCMC algorithm posterior approximations against the true analytical Bayesian posterior. This analysis isolates **approximation quality** from **exploration strategy** by running all algorithms on identical data.
**Key insight:** Thompson Sampling theory assumes sampling from the true posterior π*_t. This tool quantifies how well MCMC approximations π̃_t match π*_t.
### Quick Start
Run posterior analysis with default algorithms:
```bash
python posterior_analysis.py
```
This will:
- Generate fixed synthetic data (6 arms, 20 dimensions, 2000 timesteps)
- Run LinTS, LMCTS, FGLMCTS, MALATS, and PLMCTS on identical data
- Compute true analytical posteriors for each arm
- Create 2D scatter plots comparing true (green) vs. algorithm (red) posteriors
- Calculate Wasserstein distances quantifying approximation quality
### Customization
**Select specific algorithms:**
```bash
python posterior_analysis.py --algorithms LinTS LMCTS MALATS
```
**Change random seed:**
```bash
python posterior_analysis.py --seed 42
```
**Available algorithms:**
- `LinTS` - Analytical Thompson Sampling (baseline)
- `LMCTS` - Langevin Monte Carlo TS
- `FGLMCTS` - Feel-Good LMC-TS
- `SFGLMCTS` - Smoothed Feel-Good LMC-TS
- `MALATS` - Metropolis-Adjusted Langevin
- `FGMALATS` - Feel-Good MALA-TS
- `SFGMALATS` - Smoothed Feel-Good MALA-TS
- `PLMCTS` - Preconditioned LMC-TS
- `PFGLMCTS` - Preconditioned Feel-Good LMC-TS
- `PSFGLMCTS` - Preconditioned Smoothed Feel-Good LMC-TS
- `HMCTS` - Hamiltonian Monte Carlo TS
- `FGHMCTS`, `SFGHMCTS`, `PHMCTS`, `PFGHMCTS`, `PSFGHMCTS` - HMC variants
### Configuration
Edit parameters in `posterior_analysis.py` (lines 31-38):
```python
K_ARMS = 6 # Number of arms
D_DIM = 20 # Context dimension
LAMBDA_PRIOR = 1.0 # Prior precision
SIGMA_REWARD = 0.5 # Reward noise
T_HORIZON = 2000 # Time horizon
N_POSTERIOR_SAMPLES = 1500 # Samples for visualization
ETA = 1.0 # Inverse temperature
CORRELATED_CONTEXTS = True # True: elliptical, False: circular posteriors
```
### Output Structure
Results are saved in `posterior_analysis_YYYYMMDD_HHMMSS/`:
```
posterior_analysis_20251023_100530/
├── synthetic_data.pt # Fixed data used by all algorithms
├── results.json # Wasserstein distances and play counts
├── LinTS_posterior_comparison.png # 1×6 grid: true (green) vs. alg (red)
├── LMCTS_posterior_comparison.png
├── MALATS_posterior_comparison.png
└── ...
```
### Interpreting Results
**Visualization (PNG files):**
- **1×6 grid**: One subplot per arm showing β₁ vs β₂ projection
- **Green scatter**: 1500 samples from true analytical posterior
- **Red scatter**: 1500 samples from algorithm's posterior
- **Good approximation**: Red and green overlap
- **Poor approximation**: Red shifted or wrong shape
- **Under-exploration**: Sparse or missing red samples
**Metrics (results.json):**
```json
{
"LMCTS": {
"wasserstein_distances": [0.23, 0.34, 0.18, 0.56, 0.29, 1.23],
"mean_wasserstein": 0.468,
"num_plays_per_arm": [423, 312, 589, 245, 389, 42]
}
}
```
- **Wasserstein distance < 0.3**: Excellent approximation
- **0.3 < W < 0.7**: Good approximation
- **W > 1.0**: Poor approximation
- **W = NaN**: Arm never played
### Testing
Run unit tests to verify core functionality:
```bash
python -m pytest test_posterior_analysis.py -v
```
Or with unittest:
```bash
python test_posterior_analysis.py
```
Tests cover:
- Data generation (correlated/uncorrelated)
- True posterior computation
- Feature map correctness
- Sampling procedures
- Wasserstein distance calculation
### Use Cases
1. **Algorithm Development**: Verify new MCMC variants maintain accurate posteriors
2. **Hyperparameter Tuning**: Check if step sizes / burn-in periods affect approximation quality
3. **Failure Mode Diagnosis**: Distinguish under-exploration from poor MCMC convergence
4. **Computational Trade-offs**: Evaluate if preconditioned methods justify extra cost
### Mathematical Background
For linear bandits with reward model r_t = X_t^T β_i + ε_t, the posterior is:
```
Prior: β_i ~ N(0, λ^-1 I)
Posterior: β_i | D_t ~ N(μ_post, Σ_post)
Σ_post^-1 = λI + (η/σ²) Σ X_s X_s^T
μ_post = Σ_post · (η/σ²) · Σ X_s r_s
```
This closed-form solution serves as ground truth. MCMC algorithms approximate this through sampling procedures (Langevin, MALA, HMC).
## Weights & Biases Integration
The code is integrated with Weights & Biases for experiment tracking. To use it:
1. Install wandb: `pip install wandb`
2. Log in: `wandb login`
3. Run your experiments - results will be logged to your W&B account
## Testing
### Running Tests
We provide comprehensive unit tests for the posterior analysis functionality:
```bash
# Quick test run
make test
# Verbose output
make test-verbose
# Skip slow tests
make test-quick
```
Or directly with pytest:
```bash
pytest test_posterior_analysis.py -v
```
### Test Coverage
Tests validate:
- ✅ Data generation (correlated/uncorrelated contexts)
- ✅ True posterior computation (Bayesian linear regression)
- ✅ Block diagonal feature maps
- ✅ Posterior sampling procedures
- ✅ Wasserstein distance calculation
- ✅ Complete pipeline integration
See [TESTING.md](TESTING.md) for detailed testing documentation.
## Development Workflow
### Using Make Commands
```bash
make install # Install dependencies
make test # Run tests
make posterior-analysis # Run posterior analysis
make build # Build distribution packages
make upload-test # Upload to TestPyPI
make update-version # Update package version (interactive)
make clean # Clean generated files
```
### Updating Package Version
To release a new version:
```bash
# Automated (recommended)
make update-version
# Or manual: update version in setup.py, pyproject.toml, src/__init__.py
# Then: make clean-all && make build && make upload
```
See [VERSION_UPDATE_GUIDE.md](VERSION_UPDATE_GUIDE.md) for complete instructions.
### Adding New Agents
To add a new agent:
1. Create a new class in `src/MCMC.py` inheriting from the base agent class
2. Implement the required methods (`choose_arm`, `update`, etc.)
3. Add the agent to the `format_agent` function in `run.py`
4. Create a configuration file in the appropriate `config/` subdirectory
5. Add tests if implementing new sampling mechanisms
## Citation
If you use this code in your research, please consider citing our paper:
@article{anand2025feelgoodthompsonsamplingcontextual,
title={Feel-Good Thompson Sampling for Contextual Bandits: a Markov Chain Monte Carlo Showdown},
author={Emile Anand and Sarah Liaw},
year={2025},
eprint={2507.15290},
archivePrefix={arXiv},
primaryClass={cs.LG},
url={[https://arxiv.org/abs/2507.15290](https://arxiv.org/abs/2507.15290)},
}
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"description": "# Feel-Good Thompson Sampling for Contextual Bandits: a Markov Chain Monte Carlo Showdown\n\nThis repository implements various MCMC-based contextual bandit algorithms.\n\n## Features\n\n- **Algorithms**:\n - Langevin Monte Carlo (LMC)\n - Underdamped Langevin Monte Carlo (ULMC)\n - Metropolis-Adjusted Langevin Algorithm (MALA)\n - Hamiltonian Monte Carlo (HMC)\n - Epsilon-Greedy\n - Upper-Confidence-Bound (UCB)\n - Neural Thompson Sampling (NTS)\n - Linear Thompson Sampling (LTS)\n - Neural Upper-Confidence-Bound (NUCB)\n - Neural Greedy (NG)\n - And numerous variants with Feel-Good and smoothed Feel-Good exploration terms\n\n- **Environments**:\n - Linear bandits\n - Logistic bandits\n - Wheel bandit problem\n - Neural bandits\n\n## Installation\n\n### Option 1: Install from PyPI (Recommended)\n\n```bash\npip install ctx-bandits-mcmc\n```\n\nWith optional dependencies:\n```bash\n# For development tools\npip install ctx-bandits-mcmc[dev]\n\n# For neural bandit experiments \npip install ctx-bandits-mcmc[neural]\n\n# All optional dependencies\npip install ctx-bandits-mcmc[dev,neural]\n```\n\n### Option 2: Install from Source\n\n```bash\n# Clone the repository\ngit clone https://github.com/SarahLiaw/ctx-bandits-mcmc-showdown.git\ncd ctx-bandits-mcmc-showdown\n\n# Install the package\npip install .\n\n# Or install in editable mode for development\npip install -e .[dev]\n```\n\n### Option 3: Install from GitHub\n\n```bash\npip install git+https://github.com/SarahLiaw/ctx-bandits-mcmc-showdown.git\n```\n\nFor detailed installation instructions, platform-specific notes, and troubleshooting, see [INSTALL.md](INSTALL.md).\n\n## Quick Start\n\n### Running Linear Bandit Experiments\n\nTo run a linear bandit experiment with the LMC-TS agent:\n\n```bash\npython3 run.py --config_path config/linear/lmcts.json\n```\n\n### Running Wheel Bandit Experiments\n\nTo run the wheel bandit experiment with the ULMC agent:\n\n```bash\npython3 run_all_wheel_agents.py --agents ulmc --num_trials 1\n```\n\n### Batch Running Multiple Experiments\n\nTo run multiple experiments with different seeds:\n\n```bash\npython3 run_linear_batch.py --n_seeds 5\n```\n\n## Configuration\n\nConfiguration files are stored in the `config/` directory, organized by environment type (linear, logistic, wheel, neural). Each agent has its own configuration file with hyperparameters.\n\n## Results\n\nResults are saved in the `results/` directory by default. The directory structure is:\n\n```\nresults/\n \u251c\u2500\u2500 linear/\n \u251c\u2500\u2500 logistic/\n \u2514\u2500\u2500 wheel/\n \u2514\u2500\u2500 neural/\n```\n\n## Posterior Distribution Quality Analysis\n\n### Overview\n\nThe `posterior_analysis.py` script provides a controlled comparison of MCMC algorithm posterior approximations against the true analytical Bayesian posterior. This analysis isolates **approximation quality** from **exploration strategy** by running all algorithms on identical data.\n\n**Key insight:** Thompson Sampling theory assumes sampling from the true posterior \u03c0*_t. This tool quantifies how well MCMC approximations \u03c0\u0303_t match \u03c0*_t.\n\n### Quick Start\n\nRun posterior analysis with default algorithms:\n\n```bash\npython posterior_analysis.py\n```\n\nThis will:\n- Generate fixed synthetic data (6 arms, 20 dimensions, 2000 timesteps)\n- Run LinTS, LMCTS, FGLMCTS, MALATS, and PLMCTS on identical data\n- Compute true analytical posteriors for each arm\n- Create 2D scatter plots comparing true (green) vs. algorithm (red) posteriors\n- Calculate Wasserstein distances quantifying approximation quality\n\n### Customization\n\n**Select specific algorithms:**\n```bash\npython posterior_analysis.py --algorithms LinTS LMCTS MALATS\n```\n\n**Change random seed:**\n```bash\npython posterior_analysis.py --seed 42\n```\n\n**Available algorithms:**\n- `LinTS` - Analytical Thompson Sampling (baseline)\n- `LMCTS` - Langevin Monte Carlo TS\n- `FGLMCTS` - Feel-Good LMC-TS\n- `SFGLMCTS` - Smoothed Feel-Good LMC-TS\n- `MALATS` - Metropolis-Adjusted Langevin\n- `FGMALATS` - Feel-Good MALA-TS\n- `SFGMALATS` - Smoothed Feel-Good MALA-TS\n- `PLMCTS` - Preconditioned LMC-TS\n- `PFGLMCTS` - Preconditioned Feel-Good LMC-TS\n- `PSFGLMCTS` - Preconditioned Smoothed Feel-Good LMC-TS\n- `HMCTS` - Hamiltonian Monte Carlo TS\n- `FGHMCTS`, `SFGHMCTS`, `PHMCTS`, `PFGHMCTS`, `PSFGHMCTS` - HMC variants\n\n### Configuration\n\nEdit parameters in `posterior_analysis.py` (lines 31-38):\n\n```python\nK_ARMS = 6 # Number of arms\nD_DIM = 20 # Context dimension\nLAMBDA_PRIOR = 1.0 # Prior precision\nSIGMA_REWARD = 0.5 # Reward noise\nT_HORIZON = 2000 # Time horizon\nN_POSTERIOR_SAMPLES = 1500 # Samples for visualization\nETA = 1.0 # Inverse temperature\nCORRELATED_CONTEXTS = True # True: elliptical, False: circular posteriors\n```\n\n### Output Structure\n\nResults are saved in `posterior_analysis_YYYYMMDD_HHMMSS/`:\n\n```\nposterior_analysis_20251023_100530/\n\u251c\u2500\u2500 synthetic_data.pt # Fixed data used by all algorithms\n\u251c\u2500\u2500 results.json # Wasserstein distances and play counts\n\u251c\u2500\u2500 LinTS_posterior_comparison.png # 1\u00d76 grid: true (green) vs. alg (red)\n\u251c\u2500\u2500 LMCTS_posterior_comparison.png\n\u251c\u2500\u2500 MALATS_posterior_comparison.png\n\u2514\u2500\u2500 ...\n```\n\n### Interpreting Results\n\n**Visualization (PNG files):**\n- **1\u00d76 grid**: One subplot per arm showing \u03b2\u2081 vs \u03b2\u2082 projection\n- **Green scatter**: 1500 samples from true analytical posterior\n- **Red scatter**: 1500 samples from algorithm's posterior\n- **Good approximation**: Red and green overlap\n- **Poor approximation**: Red shifted or wrong shape\n- **Under-exploration**: Sparse or missing red samples\n\n**Metrics (results.json):**\n```json\n{\n \"LMCTS\": {\n \"wasserstein_distances\": [0.23, 0.34, 0.18, 0.56, 0.29, 1.23],\n \"mean_wasserstein\": 0.468,\n \"num_plays_per_arm\": [423, 312, 589, 245, 389, 42]\n }\n}\n```\n\n- **Wasserstein distance < 0.3**: Excellent approximation\n- **0.3 < W < 0.7**: Good approximation\n- **W > 1.0**: Poor approximation\n- **W = NaN**: Arm never played\n\n### Testing\n\nRun unit tests to verify core functionality:\n\n```bash\npython -m pytest test_posterior_analysis.py -v\n```\n\nOr with unittest:\n\n```bash\npython test_posterior_analysis.py\n```\n\nTests cover:\n- Data generation (correlated/uncorrelated)\n- True posterior computation\n- Feature map correctness\n- Sampling procedures\n- Wasserstein distance calculation\n\n### Use Cases\n\n1. **Algorithm Development**: Verify new MCMC variants maintain accurate posteriors\n2. **Hyperparameter Tuning**: Check if step sizes / burn-in periods affect approximation quality\n3. **Failure Mode Diagnosis**: Distinguish under-exploration from poor MCMC convergence\n4. **Computational Trade-offs**: Evaluate if preconditioned methods justify extra cost\n\n### Mathematical Background\n\nFor linear bandits with reward model r_t = X_t^T \u03b2_i + \u03b5_t, the posterior is:\n\n```\nPrior: \u03b2_i ~ N(0, \u03bb^-1 I)\nPosterior: \u03b2_i | D_t ~ N(\u03bc_post, \u03a3_post)\n\n\u03a3_post^-1 = \u03bbI + (\u03b7/\u03c3\u00b2) \u03a3 X_s X_s^T\n\u03bc_post = \u03a3_post \u00b7 (\u03b7/\u03c3\u00b2) \u00b7 \u03a3 X_s r_s\n```\n\nThis closed-form solution serves as ground truth. MCMC algorithms approximate this through sampling procedures (Langevin, MALA, HMC).\n\n## Weights & Biases Integration\n\nThe code is integrated with Weights & Biases for experiment tracking. To use it:\n\n1. Install wandb: `pip install wandb`\n2. Log in: `wandb login`\n3. Run your experiments - results will be logged to your W&B account\n\n## Testing\n\n### Running Tests\n\nWe provide comprehensive unit tests for the posterior analysis functionality:\n\n```bash\n# Quick test run\nmake test\n\n# Verbose output\nmake test-verbose\n\n# Skip slow tests\nmake test-quick\n```\n\nOr directly with pytest:\n```bash\npytest test_posterior_analysis.py -v\n```\n\n### Test Coverage\n\nTests validate:\n- \u2705 Data generation (correlated/uncorrelated contexts)\n- \u2705 True posterior computation (Bayesian linear regression)\n- \u2705 Block diagonal feature maps\n- \u2705 Posterior sampling procedures\n- \u2705 Wasserstein distance calculation\n- \u2705 Complete pipeline integration\n\nSee [TESTING.md](TESTING.md) for detailed testing documentation.\n\n## Development Workflow\n\n### Using Make Commands\n\n```bash\nmake install # Install dependencies\nmake test # Run tests\nmake posterior-analysis # Run posterior analysis\nmake build # Build distribution packages\nmake upload-test # Upload to TestPyPI\nmake update-version # Update package version (interactive)\nmake clean # Clean generated files\n```\n\n### Updating Package Version\n\nTo release a new version:\n\n```bash\n# Automated (recommended)\nmake update-version\n\n# Or manual: update version in setup.py, pyproject.toml, src/__init__.py\n# Then: make clean-all && make build && make upload\n```\n\nSee [VERSION_UPDATE_GUIDE.md](VERSION_UPDATE_GUIDE.md) for complete instructions.\n\n### Adding New Agents\n\nTo add a new agent:\n\n1. Create a new class in `src/MCMC.py` inheriting from the base agent class\n2. Implement the required methods (`choose_arm`, `update`, etc.)\n3. Add the agent to the `format_agent` function in `run.py`\n4. Create a configuration file in the appropriate `config/` subdirectory\n5. Add tests if implementing new sampling mechanisms\n\n## Citation\n\nIf you use this code in your research, please consider citing our paper:\n\n@article{anand2025feelgoodthompsonsamplingcontextual,\n title={Feel-Good Thompson Sampling for Contextual Bandits: a Markov Chain Monte Carlo Showdown}, \n author={Emile Anand and Sarah Liaw},\n year={2025},\n eprint={2507.15290},\n archivePrefix={arXiv},\n primaryClass={cs.LG},\n url={[https://arxiv.org/abs/2507.15290](https://arxiv.org/abs/2507.15290)}, \n}\n",
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