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-# ITPAL JAX
-Its bindings into ITPAL, written in/for jax. Thats it. End of README.
+<h1 align="center">
+  <img src='./itpal_jax.svg' width="250px">
+  <br>
+  <b>ITPAL JAX</b>
+  <br>
+</h1>
+
+JAX bindings and native implementations of differentiable trust region projections for Gaussian policies. The KL projection is handled by [ITPAL](https://github.com/ALRhub/ITPAL)'s C++ implementation, while Wasserstein and Frobenius projections are implemented in JAX. These projections provide exact solutions for trust region constraints, unlike approximate methods like PPO.
+
+## Features
+- Multiple projection types:
+  - KL (Kullback-Leibler divergence)
+  - Wasserstein (only diagonal covariance)
+  - Frobenius (wip, not tested)
+  - Identity (no projection)
+- Support for both diagonal and full covariance Gaussians (induced from cholesky decomposition)
+- Contextual and non-contextual standard deviations (non-contextual means all standard deviations in batch are expected to be the same)
+
+## Installation
+
+```bash
+python3.10 -m venv .venv # newer versions have issues with ITPAL...
+source .venv/bin/activate
+pip install -e .
+# install itpal (by e.g. copying the .so file into site packages for the venv)
+```
+## Usage
+
+```python
+import jax.numpy as jnp
+from itpal_jax import KLProjection
+
+# Create projector
+proj = KLProjection(
+    mean_bound=0.1,        # KL bound for mean
+    cov_bound=0.1,         # KL bound for covariance
+    contextual_std=True,   # Whether to use contextual standard deviations
+    full_cov=False         # Whether to use full covariance matrix
+)
+
+# Project Gaussian parameters
+new_params = {
+    "loc": jnp.array([[1.0, -1.0]]),      # mean
+    "scale": jnp.array([[0.5, 0.5]])      # standard deviations
+}
+old_params = {
+    "loc": jnp.zeros((1, 2)),
+    "scale": jnp.ones((1, 2)) * 0.3
+}
+
+# Get projected parameters
+proj_params = proj.project(new_params, old_params)
+
+# Get trust region loss
+loss = proj.get_trust_region_loss(new_params, proj_params)
+```
+
+## Testing
+
+```bash
+pytest tests/test_projections.py
+```
+
+*Note*: The test suite verifies:
+
+1. All projections run without errors and maintain basic properties (shapes, positive definiteness)
+2. KL bounds are actually (approximately) met for:
+   - KL projection (both diagonal and full covariance)
+   - Wasserstein projection (diagonal covariance only)
+3. Gradients can be computed through all projections:
+   - Both through projection operation and trust region loss
+   - Gradients have correct shapes and are finite
\ No newline at end of file