- The paper presents the MIPS estimator, which leverages action embeddings to reduce bias and variance in off-policy evaluation for expansive action spaces.
- It reshapes importance weighting by marginalizing over the embedding space, maintaining unbiased estimates even with support deficiencies.
- Empirical results on synthetic and real-world datasets highlight MIPS's robust performance improvements over traditional IPS-based methods.
Off-Policy Evaluation for Large Action Spaces via Embeddings
This paper presents a methodological advancement in off-policy evaluation (OPE) for contextual bandits where the action space is expansive. The prevalent challenge addressed is the high bias and variance associated with existing OPE estimators that primarily rely on inverse propensity score (IPS) weighting when the number of actions is substantial. This research proposes the Marginalized IPS (MIPS) estimator, leveraging action embeddings to provide structure in the action space, thereby improving evaluation accuracy.
Core Contributions
The authors identify two critical limitations in conventional IPS-based estimators when applied to large action spaces: the impractical variance caused by the wide range of importance weights and the high bias introduced by support deficiencies. They propose using additional information in the form of action embeddings, which are assumed to mediate every possible effect of an action on the reward.
The MIPS estimator introduces marginalized importance weights, calculated over the action embedding space rather than the action space itself. This shift enables MIPS to maintain unbiasedness even when the action space lacks common support between logging and target policies, provided there is sufficient common support within the embedding space.
Theoretical Insights
The paper rigorously analyzes the conditions under which MIPS can outperform traditional estimators. Key theoretical insights include:
- Unbiased estimation: MIPS remains unbiased under common embedding support and no direct action effect assumptions.
- Variance reduction: The paper demonstrates that MIPS consistently achieves lower variance compared to conventional IPS, particularly advantageous in settings with numerous possible actions.
- Bias-variance trade-off: The research explores the impact of embedding dimension quality on the estimator's bias and variance, noting that strategic selection of embedding dimensions can optimize mean squared error (MSE) by intentionally introducing a controlled bias.
Empirical Evaluation
Empirical evaluations are conducted using both synthetic data and real-world data from an online fashion platform. The experiments on synthetic datasets exhibit a substantial MSE improvement by MIPS over existing OPE estimators, particularly as the number of actions increases. In real-world scenarios, MIPS demonstrates robust performance enhancements, showcasing its applicability in practical settings.
Practical and Theoretical Implications
The shift to marginalized importance weights using embeddings introduces several implications:
- Practical benefits: MIPS extends the applicability of OPE to environments with expansive action spaces, mitigating the variance and bias issues that have long constrained traditional approaches.
- Theoretical implications: The deployment of action embeddings aligns with emerging approaches in AI that utilize structured representations to manage complexity and reduce sample inefficiencies.
Future Directions
The paper sets the stage for further exploration into how action embeddings can be effectively optimized or learned to enhance the performance of MIPS. Areas for future research include refining the estimation of marginal importance weights and extending the framework to reinforcement learning settings where action spaces continue to grow.
In conclusion, this work provides significant insights into the use of action embeddings for off-policy evaluation, representing an important step in addressing the challenges posed by large action spaces. The proposed MIPS estimator not only enhances theoretical understanding but also offers tangible improvements for real-world applications in AI and machine learning.