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RLax (pronounced "relax") is a library built on top of JAX that exposes useful building blocks for implementing reinforcement learning agents.


RLax can be installed with pip directly from github, with the following command:

pip install git+git://

All RLax code may then be just in time compiled for different hardware (e.g. CPU, GPU, TPU) using jax.jit.

In order to run the examples/ you will also need to install haiku and bsuite.


The operations and functions provided are not complete algorithms, but implementations of reinforcement learning specific mathematical operations that are needed when building fully-functional agents.

See examples/ for an example of using some of the functions in RLax to implement a Q-learning agent capable of learning to play Catch (a common unit-test for agent learning in the reinforcement learning literature).

See file-level and function-level doc-strings for the documentation of these functions and for references to the papers that introduced and/or used them.


Reinforcement learning studies the problem of a learning system (the agent), which must learn to interact with the universe it is embedded in (the environment).

Agent and environment interact on discrete steps. On each step the agent selects an action, and is provided in return a (partial) snapshot of the state of the environment (the observation), and a scalar feedback signal (the reward).

The behaviour of the agent is characterized by a probability distribution over actions, conditioned on past observations of the environment (the policy). The agents seeks a policy that, from any given step, maximises the discounted cumulative reward that will be collected from that point onwards (the return).

Often the agent policy or the environment dynamics itself are stochastic. In this case the return is a random variable, and the optimal agent's policy is typically more precisely specified as a policy that maximises the expectation of the return (the value), under the agent's and environment's stochasticity.

Reinforcement Learning Algorithms

There are three prototypical families of reinforcement learning algorithms:

  1. those that estimate the value of states and actions, and infer a policy by inspection (e.g. by selecting the action with highest estimated value)
  2. those that learn a model of the environment (capable of predicting the observations and rewards) and infer a policy via planning.
  3. those that parameterize a policy that can be directly executed,

In any case, policies, values or models are just functions. In deep reinforcement learning such functions are represented by a neural network. In this setting, it is common to formulate reinforcement learning updates as differentiable pseudo-loss functions (analogously to (un-)supervised learning). Under automatic differentiation, the original update rule is recovered.

Note however, that in particular, the updates are only valid if the input data is sampled in the correct manner. For example, a policy gradient loss is only valid if the input trajectory is an unbiased sample from the current policy; i.e. the data are on-policy. The library cannot check or enforce such constraints. Links to papers describing how each operation is used are however provided in the functions' doc-strings.

Naming Conventions and Developer Guidelines

We define functions and operations for agents interacting with a single stream of experience. The JAX construct vmap can be used to apply these same functions to batches (e.g. to support replay and parallel data generation).

Many functions consider policies, actions, rewards, values, in consecutive timesteps in order to compute their outputs. In this case the suffix _t and tm1 is often to clarify on which step each input was generated, e.g:

  • q_tm1: the action value in the source state of a transition.
  • a_tm1: the action that was selected in the source state.
  • r_t: the resulting rewards collected in the destination state.
  • discount_t: the discount associated with a transition.
  • q_t: the action values in the destination state.

Extensive testing is provided for each function. All tests should also verify the output of rlax functions when compiled to XLA using jax.jit and when performing batch operations using jax.vmap.

Citing RLax

To cite this repository:

  author = {David Budden and Matteo Hessel and John Quan and Steven Kapturowski},
  title = {{RL}ax: {R}einforcement {L}earning in {JAX}},
  url = {},
  version = {0.0.1a0},
  year = {2020},

In this bibtex entry, the version number is intended to be from rlax/, and the year corresponds to the project's open-source release.

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