Cesar Salcedo

Posterior Sampling for Reinforcement Learning (PSRL)

Jul 24, 2023

With the Reinforcement Learning Theory group at the University of Alberta and Alberta Machine Intelligence Institute (Amii). Funded by the Emerging Leaders in the Americas (ELAP) scholarship.
During my research internship at the University of Alberta, I was able to work on option discovery for long-horizon MDPs in the context of reinforcement learning theory research. A side project I set myself to accomplish for this purpose was replicating the experimental results from the paper (More) Efficient Reinforcement Learning via Posterior Sampling, which introduces Posterior Sampling for Reinforcement Learning (PSRL) algorithm. This article gathers some results obtained from this experience.
We first set on the task of reproducing the results from Figure 2 in the paper, but this time extending both the evaluation time by an order of magnitude and also evaluating UCRL2, not only KL-UCRL and PSRL. The following plot is the result of this experiment.
Regret for PSRL, UCRL2, and KL-UCRL on 100000 steps of RiverSwim environment.
Regret for PSRL, UCRL2, and KL-UCRL on 100000 steps of RiverSwim environment.
We later extended the evaluation to other MDPs with more structure, such as gridworlds. In particular, we considered the following gridworlds with four and two rooms.
Gridworld environments: a) FourRoom, and b) TwoRoom. The blue cell represents the initial state in the environment, while the green cell represents the terminal state. All states give a reward of 0 to the agent except for the terminal state, which has a reward of 1.
Gridworld environments: a) FourRoom, and b) TwoRoom. The blue cell represents the initial state in the environment, while the green cell represents the terminal state. All states give a reward of 0 to the agent except for the terminal state, which has a reward of 1.
The trajectory followed by the agent while training was recorded for later analysis. This makes it possible to generate the following video
Over the course of 100000 training steps we can plot the number of times a state has been visited in total, namely the empirical state visitation.
Empirical state visitation.
Empirical state visitation.
Note that at the beginning of training the agent doesn't know where the goal is, so it takes actions at random. However, the agent eventually finds the reward at the bottom right room of the gridworld.
Expected reward.
Expected reward.
After training, the agent has learnt both an state-value function and action-value function, which are observed to reflect the correct location of the reward.
Action-value function.
Action-value function.
State-value function.
State-value function.

References

csalcedo001/psrlPSRL on RiverSwim and Random MDP - Weights & Biases