Vanilla Policy Gradient

Background

(Previously: Introduction to RL, Part 3)

The key idea underlying policy gradients is to push up the probabilities of actions that lead to higher return, and push down the probabilities of actions that lead to lower return, until you arrive at the optimal policy.

Quick Facts

  • VPG is an on-policy algorithm.
  • VPG can be used for environments with either discrete or continuous action spaces.
  • The Spinning Up implementation of VPG supports parallelization with MPI.

Key Equations

Let \pi_{\theta} denote a policy with parameters \theta, and J(\pi_{\theta}) denote the expected finite-horizon undiscounted return of the policy. The gradient of J(\pi_{\theta}) is

\nabla_{\theta} J(\pi_{\theta}) = \underE{\tau \sim \pi_{\theta}}{
    \sum_{t=0}^{T} \nabla_{\theta} \log \pi_{\theta}(a_t|s_t) A^{\pi_{\theta}}(s_t,a_t)
    },

where \tau is a trajectory and A^{\pi_{\theta}} is the advantage function for the current policy.

The policy gradient algorithm works by updating policy parameters via stochastic gradient ascent on policy performance:

\theta_{k+1} = \theta_k + \alpha \nabla_{\theta} J(\pi_{\theta_k})

Policy gradient implementations typically compute advantage function estimates based on the infinite-horizon discounted return, despite otherwise using the finite-horizon undiscounted policy gradient formula.

Exploration vs. Exploitation

VPG trains a stochastic policy in an on-policy way. This means that it explores by sampling actions according to the latest version of its stochastic policy. The amount of randomness in action selection depends on both initial conditions and the training procedure. Over the course of training, the policy typically becomes progressively less random, as the update rule encourages it to exploit rewards that it has already found. This may cause the policy to get trapped in local optima.

Documentation

spinup.vpg(env_fn, actor_critic=<function mlp_actor_critic>, ac_kwargs={}, seed=0, steps_per_epoch=4000, epochs=50, gamma=0.99, pi_lr=0.0003, vf_lr=0.001, train_v_iters=80, lam=0.97, max_ep_len=1000, logger_kwargs={}, save_freq=10)[source]
Parameters:
  • env_fn – A function which creates a copy of the environment. The environment must satisfy the OpenAI Gym API.
  • actor_critic

    A function which takes in placeholder symbols for state, x_ph, and action, a_ph, and returns the main outputs from the agent’s Tensorflow computation graph:

    Symbol Shape Description
    pi (batch, act_dim)
    Samples actions from policy given
    states.
    logp (batch,)
    Gives log probability, according to
    the policy, of taking actions a_ph
    in states x_ph.
    logp_pi (batch,)
    Gives log probability, according to
    the policy, of the action sampled by
    pi.
    v (batch,)
    Gives the value estimate for states
    in x_ph. (Critical: make sure
    to flatten this!)
  • ac_kwargs (dict) – Any kwargs appropriate for the actor_critic function you provided to VPG.
  • seed (int) – Seed for random number generators.
  • steps_per_epoch (int) – Number of steps of interaction (state-action pairs) for the agent and the environment in each epoch.
  • epochs (int) – Number of epochs of interaction (equivalent to number of policy updates) to perform.
  • gamma (float) – Discount factor. (Always between 0 and 1.)
  • pi_lr (float) – Learning rate for policy optimizer.
  • vf_lr (float) – Learning rate for value function optimizer.
  • train_v_iters (int) – Number of gradient descent steps to take on value function per epoch.
  • lam (float) – Lambda for GAE-Lambda. (Always between 0 and 1, close to 1.)
  • max_ep_len (int) – Maximum length of trajectory / episode / rollout.
  • logger_kwargs (dict) – Keyword args for EpochLogger.
  • save_freq (int) – How often (in terms of gap between epochs) to save the current policy and value function.

Saved Model Contents

The computation graph saved by the logger includes:

Key Value
x Tensorflow placeholder for state input.
pi Samples an action from the agent, conditioned on states in x.
v Gives value estimate for states in x.

This saved model can be accessed either by

References

Why These Papers?

Sutton 2000 is included because it is a timeless classic of reinforcement learning theory, and contains references to the earlier work which led to modern policy gradients. Schulman 2016(a) is included because Chapter 2 contains a lucid introduction to the theory of policy gradient algorithms, including pseudocode. Duan 2016 is a clear, recent benchmark paper that shows how vanilla policy gradient in the deep RL setting (eg with neural network policies and Adam as the optimizer) compares with other deep RL algorithms. Schulman 2016(b) is included because our implementation of VPG makes use of Generalized Advantage Estimation for computing the policy gradient.