cpomdp 0.2.0

Continuous active inference for Python — the continuous-state sibling of pymdp.

cpomdp

Continuous active inference for Python. The continuous-state sibling of pymdp.

pymdp is great, but it speaks in discrete states. A lot of the world isn't discrete. Positions, velocities, temperatures, the kinds of things you'd actually want an agent to track and steer, don't come in neat little categories. cpomdp fills that gap. You hand it a linear-Gaussian model of how the world moves and what you can see of it, and you get back an agent that perceives and acts in the same infer_states / sample_action loop pymdp users already know.

That's the whole idea: keep the pymdp muscle memory, swap the discrete machinery underneath for continuous.

Example

A bacillus seeking food — the continuous-state answer to pymdp's mouse-seeking-cheese. The body sits at the true hidden state; the orange + is where the agent believes it is (belief.mean); the blue ellipse is its uncertainty (belief.cov), wide at first and shrinking as the Kalman filter locks on; the star is the food (the goal the LQR controller steers toward). It perceives, acts, and arrives.

Reproduce it with examples/bacillus_seeking_food.py (pip install matplotlib pillow).

Install

pip install cpomdp

Or the latest from source:

pip install git+https://github.com/DanBoringName/cpomdp

That's all you need for normal use. There's also an optional RxInfer (Julia) backend that the test suite leans on as a correctness oracle. You almost certainly don't need it, but if you want it:

pip install "cpomdp[rxinfer]"

It pulls in a Julia bridge and bootstraps itself the first time you use it.

Quickstart

Here's an agent steering a point mass to a target. It can push the mass and it can see where the mass is, but it never sees the velocity. The filter has to work that out from how the position moves.

import jax.numpy as jnp
from cpomdp import Agent, Belief, LinearGaussianModel

# State is [position, velocity]. A push changes velocity, velocity carries
# position along, and we only ever observe position (through a noisy sensor).
dt = 0.1
model = LinearGaussianModel(
    dynamics=[[1, dt], [0, 1]],          # velocity carries position along
    control=[[0], [dt]],                 # a push nudges velocity
    sensor_model=[[1, 0]],               # we observe position only
    dynamics_noise=jnp.eye(2) * 1e-6,
    sensor_noise=[[1e-2]],
    prior=Belief(mean=[0, 0], cov=jnp.eye(2)),
)

# Tell it where to go: sit still at position 1.
agent = Agent(model, goal=[1.0, 0.0])

true_state = jnp.array([0.0, 0.0])
for _ in range(100):
    obs = model.sensor_model @ true_state            # what the agent gets to see
    agent.infer_states(obs)                           # perceive
    action = agent.sample_action()                    # act
    true_state = model.dynamics @ true_state + model.control @ action

print(jnp.round(agent.belief.mean, 3))   # ≈ [1, 0]

Run that and the belief lands on [1, 0]. The agent worked out it was at position 1 and sitting still, which is exactly where we asked it to go, and it did it without ever seeing the velocity it had to control.

The pymdp parallel

If you've used pymdp, this table is basically the whole API:

pymdp (discrete)	cpomdp (continuous)	what it is
Agent	Agent	the stateful thing you drive
qs	belief	the posterior over the state
infer_states	infer_states	fold in an observation
sample_action	sample_action	pick an action
C	goal + goal_precision	the state you prefer, how sharply
D	model.prior	belief before you've seen anything

One honest difference. sample_action here is deterministic, not a sample from a policy posterior. For a linear-Gaussian sensor the action that minimises expected free energy turns out to be exactly the LQR optimum, so there's a single best action and that's what comes back. Same loop, exact answer. The reasoning is in DECISIONS.md (ADR-003) if you want it.

Just want to track, not act?

Leave the goal out and you get a pure tracker. infer_states still folds in observations and sharpens the belief, but sample_action will stop you, because there's nothing to steer toward.

agent = Agent(model)                  # no goal
belief = agent.infer_states([0.5])    # perceiving is fine
agent.sample_action()                 # ValueError: this Agent has no goal

What's in the box

Right now (v0.1) cpomdp handles linear-Gaussian models: Kalman filtering for perception, steady-state LQR for action. That already covers a fair bit of ground, roughly anything you'd reach for a Kalman filter to do, but it's the foundation rather than the finished house. Nonlinear models and proper epistemic (information-seeking) action are the obvious next steps.

You can swap the inference engine if you want to. KalmanBackend is the default and does the real work; RxInferBackend re-derives the same answers through Julia and exists mainly so the fast path has something independent to check itself against. Both sit behind the InferenceBackend protocol, so you can write your own.

This is pre-alpha. The API works and the maths is tested against that independent oracle, but expect things to move before 1.0.