Intrinsic Rewards for Exploration without Harm from Observational Noise: A Simulation Study Based on the Free Energy Principle

TL;DR

This work tackles exploration in reinforcement learning under observational noise by introducing hidden state curiosity derived from the Free Energy Principle. The authors implement a variational RNN forward model that encodes latent states and quantify curiosity via the KL divergence between predictive prior and posterior over these latent states, integrated into a SAC framework with entropy regularization. Through six agent types tested in biased and expanding T-maze environments, they demonstrate that entropy and curiosity jointly enhance exploration, with hidden state curiosity offering robustness against curiosity traps that degrade prediction-error-based methods. The findings suggest that FEP-informed curiosity can improve robustness and generalization in RL, potentially aligning artificial learning processes with biological principles. The study provides a scalable, per-transition curiosity measure and points to future extensions with hierarchical PV-RNNs and dynamic tuning of curiosity hyperparameters.

Abstract

In Reinforcement Learning (RL), artificial agents are trained to maximize numerical rewards by performing tasks. Exploration is essential in RL because agents must discover information before exploiting it. Two rewards encouraging efficient exploration are the entropy of action policy and curiosity for information gain. Entropy is well-established in literature, promoting randomized action selection. Curiosity is defined in a broad variety of ways in literature, promoting discovery of novel experiences. One example, prediction error curiosity, rewards agents for discovering observations they cannot accurately predict. However, such agents may be distracted by unpredictable observational noises known as curiosity traps. Based on the Free Energy Principle (FEP), this paper proposes hidden state curiosity, which rewards agents by the KL divergence between the predictive prior and posterior probabilities of latent variables. We trained six types of agents to navigate mazes: baseline agents without rewards for entropy or curiosity, and agents rewarded for entropy and/or either prediction error curiosity or hidden state curiosity. We find entropy and curiosity result in efficient exploration, especially both employed together. Notably, agents with hidden state curiosity demonstrate resilience against curiosity traps, which hinder agents with prediction error curiosity. This suggests implementing the FEP may enhance the robustness and generalization of RL models, potentially aligning the learning processes of artificial and biological agents.

Figures (11)

• Figure 1: (a) Implementing recurrent layers in an actor model and a critic model. Notice the previous action $a_{t-1}$ is implicitly included in $h^\theta_{t-1}$. (b) Implementing the forward model's hidden state $h^q$ in an actor model and a critic model. Black arrows indicate forward computations. Red arrows indicate loss functions for backpropagation.
• Figure 2: Forward model’s architecture based on VRNN. Black arrows indicate forward computations. Red arrows indicate errors for backpropagation.
• Figure 3: An agent's observation includes its current speed in meters per time step and an 8 by 8 by 4 image of what is in front of it. The image's four channels are red, green, blue (left), and distance (right). This is the agent's first observation in the biased T-maze; see figure \ref{['fig:tmaze']}.
• Figure 4: Agent starts where shown. Correct and incorrect exits are marked ✓ and X. With curiosity traps, blocks with ? change colors each step. Experiment one uses (a) biased T-Maze. Experiment two uses (b) T-maze, (c) double T-maze, (d) triple T-maze.
• Figure 5: Trajectories of agents after training in the biased T-maze. The correct exit of each maze is marked with a ✓, while each incorrect exit is marked with an X. If curiosity traps are applied, blocks marked with a ? will change to random colors with every step.