Summary

Integrate Thompson Sampling with ENNs in GFlowNets to enhance exploration and solution diversity.

Introduction

Motivation

The analysis of the related papers reveals a consistent effort to enhance the capabilities of GFlowNets, particularly in terms of improving exploration efficiency, sample diversity, and computational efficiency. However, a persistent challenge across these studies is the issue of mode collapse and efficient exploration in high-dimensional spaces. Building upon these insights, a promising research idea would involve developing a novel mechanism within the GFlowNet framework that specifically targets these challenges, potentially by integrating advanced uncertainty quantification techniques to guide exploration more effectively.

Hypothesis

Integrating Thompson Sampling with Epistemic Neural Networks into GFlowNets will significantly enhance the diversity and quality of high-reward solutions compared to using either method independently.

Research Gap

Existing research has extensively explored MC Dropout and ensemble methods for epistemic uncertainty quantification in GFlowNets, but the potential of combining Thompson Sampling with Epistemic Neural Networks (ENNs) for enhanced exploration remains underexplored. This gap is significant because leveraging Thompson Sampling's ability to explore high-uncertainty regions with ENNs' joint prediction capabilities could lead to more diverse and high-reward solution discovery in sparse-reward environments.

Hypothesis Elements

Independent variable: Integration of Thompson Sampling with Epistemic Neural Networks into GFlowNets

Comparison groups: 1) GFlowNet with Thompson Sampling only, 2) GFlowNet with Epistemic Neural Networks only, 3) GFlowNet with integrated Thompson Sampling and Epistemic Neural Networks

Baseline/control: Using Thompson Sampling or Epistemic Neural Networks independently in GFlowNets

Context/setting: Molecular design task environment with complex reward landscape

Assumptions: Thompson Sampling and ENNs can be effectively integrated within the GFlowNet architecture; diversity of solutions is crucial in complex reward structures

Timeframe: Varies by experiment mode: 100-200 iterations for mini-pilot, 1000-2000 for pilot, 10,000+ for full experiment

Measurement method: Shannon Diversity Index, number of distinct high-reward solutions, mean reward, top-k reward, and exploration efficiency

Proposed Method

Overview

This research explores the integration of Thompson Sampling with Epistemic Neural Networks (ENNs) within GFlowNets to enhance exploration efficiency and solution diversity. Thompson Sampling, known for its ability to explore high-uncertainty regions by using an ensemble of policy heads, will be combined with ENNs, which provide high-quality joint predictions and calibrated uncertainty estimates. The hypothesis posits that this integration will allow GFlowNets to better navigate sparse-reward environments by focusing exploration on under-explored regions with high potential for diverse and high-reward solutions. The expected outcome is an increase in the number of unique high-reward solutions discovered, as measured by the Shannon Diversity Index and the number of distinct high-reward solutions. This approach addresses the gap in existing research by combining the strengths of Thompson Sampling and ENNs, which have not been extensively tested together in similar contexts. The evaluation will be conducted in environments with complex reward structures, such as molecular design tasks, where the diversity of solutions is crucial.

Background

Thompson Sampling: Thompson Sampling is an exploration strategy that uses an ensemble of policy heads within a shared network architecture. Each policy head represents a different hypothesis about the environment, and a random head is selected to generate the trajectory. This method captures uncertainty through the diversity in predictions across different heads, allowing the model to explore various potential outcomes. In this experiment, Thompson Sampling will be configured to work with ENNs by selecting policy heads based on the uncertainty estimates provided by the ENNs. This integration is expected to enhance exploration by focusing on high-uncertainty regions, thereby increasing the diversity of high-reward solutions.

Epistemic Neural Networks (ENNs): ENNs are designed to produce high-quality joint predictions by integrating uncertainty estimation directly into the network architecture. They augment conventional neural networks with additional components that capture uncertainty, such as Bayesian layers or stochastic units. In this experiment, ENNs will be used to guide the selection of policy heads in Thompson Sampling, providing calibrated estimates of epistemic uncertainty. This approach is expected to improve the exploration efficiency of GFlowNets by focusing on regions of the state space where the reward distribution is not well understood, leading to the discovery of diverse high-reward solutions.

Implementation

The hypothesis will be implemented by integrating Thompson Sampling with Epistemic Neural Networks (ENNs) in the GFlowNet architecture. The ENNs will be configured to provide joint predictions and uncertainty estimates, which will guide the selection of policy heads in Thompson Sampling. The integration will involve modifying the GFlowNet's exploration strategy to incorporate ENNs' uncertainty estimates in the decision-making process. Specifically, during each exploration step, the ENNs will evaluate the uncertainty of the current state, and Thompson Sampling will select a policy head based on these estimates. The selected head will generate the trajectory, and the diversity of predictions across heads will be used to guide exploration. This setup will require building a new module that combines the outputs of ENNs with Thompson Sampling's policy selection mechanism. The data flow will involve passing state representations through the ENNs to obtain uncertainty estimates, which will then inform the selection of policy heads in Thompson Sampling. The expected outcome is an increase in the diversity and quality of high-reward solutions, as measured by the Shannon Diversity Index and the number of distinct high-reward solutions.

Experiments Plan

Operationalization Information

Please implement an experiment to test the hypothesis that integrating Thompson Sampling with Epistemic Neural Networks (ENNs) into GFlowNets will significantly enhance the diversity and quality of high-reward solutions compared to using either method independently.

Experiment Overview

This experiment will compare three approaches for exploration in GFlowNets:
1. Baseline 1: Standard GFlowNet with Thompson Sampling only
2. Baseline 2: GFlowNet with Epistemic Neural Networks only
3. Experimental: GFlowNet with integrated Thompson Sampling and Epistemic Neural Networks

The experiment should be conducted in a molecular design task environment, which provides a complex reward landscape where solution diversity is crucial.

Implementation Details

Global Settings

Implement a global variable PILOT_MODE with three possible settings: MINI_PILOT, PILOT, or FULL_EXPERIMENT. The experiment should start with MINI_PILOT mode.

MINI_PILOT: Use a very small subset of molecular design tasks (5-10 molecules) and run for a limited number of iterations (100-200) to verify code functionality. Use a small ensemble size (3 policy heads) for Thompson Sampling.
PILOT: Use a moderate subset of molecular design tasks (50-100 molecules) and run for 1000-2000 iterations. Use 5 policy heads for Thompson Sampling.
FULL_EXPERIMENT: Use the complete dataset of molecular design tasks and run for 10,000+ iterations with 10 policy heads for Thompson Sampling.

The experiment should run the MINI_PILOT first, then if everything looks good, proceed to the PILOT. After the PILOT completes, it should stop and not run the FULL_EXPERIMENT (a human will manually verify the results and make the change to FULL_EXPERIMENT if appropriate).

Thompson Sampling Module

Implement a Thompson Sampling module with the following components:
1. An ensemble of policy heads (neural networks) sharing a common feature extraction backbone
2. A mechanism to randomly select a policy head for each trajectory generation
3. A method to update the policy heads based on the rewards received

Epistemic Neural Network Integration

Implement the ENN component with the following features:
1. Bayesian neural network layers to estimate uncertainty
2. A method to provide calibrated uncertainty estimates for each state
3. A mechanism to use these uncertainty estimates to guide exploration

Integrated Thompson-ENN Approach

For the experimental condition, implement the integration as follows:
1. Use the ENN to evaluate the uncertainty of the current state
2. Use the uncertainty estimates to inform the selection of policy heads in Thompson Sampling
3. Weight the selection probability of each policy head based on the uncertainty estimates
4. Generate trajectories using the selected policy head

GFlowNet Framework

Use the GFlowNet framework with the following configurations:
1. State space: Molecular graphs with atoms and bonds
2. Action space: Adding/removing atoms and bonds
3. Reward function: A combination of drug-likeness scores (e.g., QED), synthetic accessibility, and target property optimization

Evaluation Metrics

Primary Metrics

Shannon Diversity Index: Calculate this for the set of generated molecules to quantify solution diversity
Number of Distinct High-Reward Solutions: Count unique solutions that achieve a reward above a predefined threshold (set this threshold as the 75th percentile of rewards in the MINI_PILOT)

Secondary Metrics

Mean Reward: Average reward across all generated solutions
Top-k Reward: Average reward of the top k% solutions
Exploration Efficiency: Number of unique high-reward solutions discovered per iteration

Experimental Protocol

Initialize all three models (Thompson Sampling only, ENN only, and Thompson-ENN integrated)
For each model, run the GFlowNet for the specified number of iterations based on the PILOT_MODE
At regular intervals (every 100 iterations for MINI_PILOT, 500 for PILOT, 1000 for FULL_EXPERIMENT), evaluate and record all metrics
Generate visualizations comparing the performance of all three approaches over time
Perform statistical analysis to determine if the differences between approaches are significant (use bootstrap resampling with 1000 resamples)

Output and Reporting

Generate plots showing the evolution of all metrics over iterations for all three approaches
Create a table summarizing the final values of all metrics for all three approaches
Report p-values from statistical tests comparing the experimental approach to each baseline
Generate visualizations of a diverse subset of high-reward molecules discovered by each approach
Save all generated molecules, their rewards, and associated metrics to CSV files
Create a comprehensive log file documenting the experiment configuration, progress, and results

Please implement this experiment with clear code organization, proper documentation, and robust error handling. The code should be modular to allow for easy modification of hyperparameters and experimental conditions.

Paper ID

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