[Paper Review] Adapting to Misspecification in Contextual Bandits with Offline Regression Oracles

Sanath Kumar Krishnamurthy, Vitor Hadad+1 more|arXiv (Cornell University)|Feb 26, 2021

Advanced Bandit Algorithms Research16 references4 citations

TL;DR

This paper proposes a contextual bandit algorithm that adapts to model misspecification by reverting to a safe policy when evidence of high misspecification error is detected. It uses only an offline regression oracle, avoiding the need for complex oracles or master algorithms, and achieves regret guarantees that gracefully degrade with increasing misspecification levels.

ABSTRACT

Computationally efficient contextual bandits are often based on estimating a predictive model of rewards given contexts and arms using past data. However, when the reward model is not well-specified, the bandit algorithm may incur unexpected regret, so recent work has focused on algorithms that are robust to misspecification. We propose a simple family of contextual bandit algorithms that adapt to misspecification error by reverting to a good safe policy when there is evidence that misspecification is causing a regret increase. Our algorithm requires only an offline regression oracle to ensure regret guarantees that gracefully degrade in terms of a measure of the average misspecification level. Compared to prior work, we attain similar regret guarantees, but we do no rely on a master algorithm, and do not require more robust oracles like online or constrained regression oracles (e.g., Foster et al. (2020a); Krishnamurthy et al. (2020)). This allows us to design algorithms for more general function approximation classes.

Motivation & Objective

• Address the problem of performance degradation in contextual bandits when the reward model is misspecified, particularly in linear or parametric models.
• Overcome the limitations of realizability-based algorithms like FALCON+ and LinUCB, which can exhibit erratic behavior and increasing regret under misspecification.
• Design a computationally efficient algorithm that maintains strong regret guarantees even when the true reward function is not in the assumed function class.
• Eliminate reliance on specialized oracles (e.g., online, constrained, or robust regression oracles) by using only standard offline regression oracles.
• Enable broader applicability to general function approximation classes by decoupling the algorithm from assumptions on the oracle's robustness.

Proposed method

• Introduce a family of contextual bandit algorithms that monitor the quality of the offline regression oracle's predictions to detect increasing misspecification error.
• When the model's prediction error exceeds a threshold, the algorithm reverts to a safe policy (e.g., uniform or behavior policy) to prevent exploitation of erroneous estimates.
• Use a confidence-based mechanism to dynamically adjust exploration vs. exploitation, relying only on the offline regression oracle for reward predictions.
• Define a measure of average misspecification error that quantifies the deviation of the true reward function from the model class, which directly influences the regret bound.
• Ensure regret guarantees degrade smoothly with increasing misspecification, maintaining performance even when the model is not well-specified.
• Avoid the use of a master algorithm or complex optimization layers, relying instead on a simple, modular design built on standard regression oracles.

Experimental results

Research questions

• RQ1 How can contextual bandit algorithms maintain performance when the assumed reward model is misspecified?
• RQ2 Can regret guarantees be preserved without requiring robust or constrained regression oracles or master algorithms?
• RQ3 What is the impact of model misspecification on the convergence and stability of existing realizability-based algorithms like FALCON+?
• RQ4 How can a safe policy be dynamically triggered based on evidence of increasing prediction error?
• RQ5 Can a simple, modular design using only offline regression oracles achieve robustness to misspecification in general function classes?

Key findings

• The proposed Safe-FALCON algorithm successfully mitigates the oscillatory regret behavior seen in FALCON+ under model misspecification, stabilizing performance over time.
• The algorithm achieves regret bounds that degrade gracefully with increasing average misspecification error, ensuring robustness even when the true reward function is not linear.
• By reverting to a safe policy when misspecification is detected, the algorithm avoids the data skewing and instability that plague realizability-based methods.
• The method maintains strong computational efficiency and does not require additional oracles beyond standard offline regression, unlike prior robust approaches.
• Empirical results show that the algorithm avoids the high regret spikes and oscillations observed in FALCON+, particularly in later epochs where model drift occurs.
• The regret bound scales with the square root of the misspecification level, providing a clear trade-off between model accuracy and performance degradation.