TLDR: This research introduces a novel approach using fully online imputation ensembles to handle missing data in real-time reinforcement learning, specifically for tabular Q-learning. The method maintains multiple imputation pathways to capture uncertainty and improve efficiency. Experiments in a Grid World environment demonstrate that these multiple imputation ensembles generally outperform single imputation and simpler baseline methods across various missingness scenarios, offering a robust and faster learning solution for online RL agents.
In the dynamic world of online reinforcement learning (RL), agents learn to make decisions in real-time to maximize rewards within an ever-changing environment. However, a significant challenge arises when this environment presents incomplete or missing data. Unlike traditional data analysis or offline learning, online RL demands immediate imputation and action, where past imputations directly influence future data collection and learning outcomes.
A new research paper, titled “Missing Data Multiple Imputation for Tabular Q-Learning in Online RL,” proposes an innovative solution: fully online imputation ensembles. Authored by Kyla Chasalow, Skyler Wu, and Susan Murphy, this work explores how maintaining multiple imputation pathways can effectively balance the need to account for uncertainty due to missing information with the crucial requirement for efficiency in online settings.
The core idea behind imputation ensembles is to generate and maintain several distinct sequences of imputed missing values. Each pathway represents a different plausible scenario for the missing states. By conditioning on these possibly imputed previous states, the system can draw new missing values, creating a chain of imputations. The researchers suggest that ensembles can help mitigate errors that might accumulate if only a single imputation pathway were used, especially if the imputation errors across pathways are not highly correlated.
The paper focuses on tabular Q-learning, a fundamental RL algorithm, to uncover the underlying dynamics and insights of their proposed method. They outline several key design choices for constructing these ensembles:
Generating Imputations
The process of probabilistically imputing missing state components requires learning models of the transition distribution. The authors consider two main approaches for updating these transition models:
- Conservative: This method learns only from fully observed data, which avoids self-reinforcement but risks discarding valuable partial observations.
- Synthetic: This approach incorporates both observed and imputed (synthetic) data counts into the learning process. While it leverages more information, it carries the risk of reinforcing incorrect data, particularly in certain missingness scenarios.
Learning Updates
With multiple imputations, a single Q-function is learned by applying a fractional learning rate sequentially across each imputation pathway. This fractional update moderates the impact of individual imputations, ensuring that their influence is distributed and diminished if they disagree, which is beneficial for representing uncertainty.
Action Selection
To encourage exploration, the agent selects its next action using a voting ensemble over the various imputed states. This means that instead of relying on a single best action from one imputed state, the agent considers the recommendations from all pathways and makes a decision based on their collective ‘vote’.
Comparison with Baselines
The researchers compared their multiple imputation (MI) variants against several simpler baseline methods:
- Random Action: Taking a random action when data is missing.
- Last Observed State (V1 & V2): Using the last fully observed state or the most recently observed value for each dimension to fill in missing information.
- Missing as a State: Treating ‘missing’ as an additional state value, effectively expanding the state space.
The experiments were conducted in an 8×8 Grid World environment, which included elements like location, categorical color, various movement actions, rewards for reaching a terminal state, penalties for stepping in ‘ponds’, and environmental stochasticity (flooding and wind). Three types of missingness mechanisms were tested: Missing Completely at Random (MCAR), Missing at Random based on COLOR (MCOLOR), and Not Missing at Random due to FOG (MFOG).
Key Findings
The results provided preliminary evidence that MI ensembles are a useful framework for online missing data RL methods. Across various missingness mechanisms and rates, MI ensembles generally outperformed single imputation and the simpler baselines in terms of maximizing reward, minimizing penalties, and reducing path length. They demonstrated greater robustness to increasing missingness rates and learned faster.
Interestingly, while both conservative and synthetic T-update MI approaches performed similarly in most cases, the synthetic updates showed potential harm in Not Missing at Random (NMAR) scenarios like the MFOG experiment. This highlights a risk where synthetic updates might reinforce incorrect data, especially when missingness itself carries a strong signal about the true state.
The ‘missing-as-state’ baseline exhibited a U-shaped performance curve under MCAR, performing worse at moderate missingness but better at very low or very high rates. This suggests that expanding the state space can be costly when missingness is uninformative, but might simplify learning when missingness is either rare or so pervasive that it effectively reduces the state space to a few common ‘missing’ patterns.
The study also found diminishing returns for increasing the number of imputation pathways (K), with K=5 showing significant gains over K=1, but K=10 offering less dramatic improvements.
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- Ensemble Sampling: A Robust Approach for Complex Online Decision-Making
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Future Directions
While these results are promising, the authors emphasize that they are preliminary and require further testing in diverse settings beyond Grid Worlds, including scenarios with infinite horizons and more complex NMAR situations. Future work could explore combining imputation with ‘missing-as-state’ approaches, investigating the impact of environment stochasticity, and developing methods for information-gathering actions in the presence of missing data.
This research offers a significant step towards developing efficient and robust online reinforcement learning agents that can effectively navigate and learn in real-world environments where data incompleteness is a constant reality. For more details, you can read the full paper here.
