Off-Policy Evaluation from Logged Human Feedback

Learning from human feedback has been central to recent advances in artificial intelligence and machine learning. Since the collection of human feedback is costly, a natural question to ask is if the new feedback always needs to collected. Or could we evaluate a new model with the human feedback on responses of another model? This motivates us to study off-policy evaluation from logged human feedback. We formalize the problem, propose both model-based and model-free estimators for policy values, and show how to optimize them. We analyze unbiasedness of our estimators and evaluate them empirically. Our estimators can predict the absolute values of evaluated policies, rank them, and be optimized.

Pretraining Decision Transformers with Reward Prediction for In-Context Multi-task Structured Bandit Learning

In this paper, we study multi-task structured bandit problem where the goal is to learn a near-optimal algorithm that minimizes cumulative regret. The tasks share a common structure and the algorithm exploits the shared structure to minimize the cumulative regret for an unseen but related test task. We use a transformer as a decision-making algorithm to learn this shared structure so as to generalize to the test task. The prior work of pretrained decision transformers like DPT requires access to the optimal action during training which may be hard in several scenarios. Diverging from these works, our learning algorithm does not need the knowledge of optimal action per task during training but predicts a reward vector for each of the actions using only the observed offline data from the diverse training tasks. Finally, during inference time, it selects action using the reward predictions employing various exploration strategies in-context for an unseen test task. Our model outperforms other SOTA methods like DPT, and Algorithmic Distillation over a series of experiments on several structured bandit problems (linear, bilinear, latent, non-linear). Interestingly, we show that our algorithm, without the knowledge of the underlying problem structure, can learn a near-optimal policy in-context by leveraging the shared structure across diverse tasks. We further extend the field of pre-trained decision transformers by showing that they can leverage unseen tasks with new actions and still learn the underlying latent structure to derive a near-optimal policy. We validate this over several experiments to show that our proposed solution is very general and has wide applications to potentially emergent online and offline strategies at test time. Finally, we theoretically analyze the performance of our algorithm and obtain generalization bounds in the in-context multi-task learning setting.

SaVeR: Optimal Data Collection Strategy for Safe Policy Evaluation in Tabular MDP

In this paper, we study safe data collection for the purpose of policy evaluation in tabular Markov decision processes (MDPs). In policy evaluation, we are given a \textit{target} policy and asked to estimate the expected cumulative reward it will obtain. Policy evaluation requires data and we are interested in the question of what \textit{behavior} policy should collect the data for the most accurate evaluation of the target policy. While prior work has considered behavior policy selection, in this paper, we additionally consider a safety constraint on the behavior policy. Namely, we assume there exists a known default policy that incurs a particular expected cost when run and we enforce that the cumulative cost of all behavior policies ran is better than a constant factor of the cost that would be incurred had we always run the default policy. We first show that there exists a class of intractable MDPs where no safe oracle algorithm with knowledge about problem parameters can efficiently collect data and satisfy the safety constraints. We then define the tractability condition for an MDP such that a safe oracle algorithm can efficiently collect data and using that we prove the first lower bound for this setting. We then introduce an algorithm SaVeR for this problem that approximates the safe oracle algorithm and bound the finite-sample mean squared error of the algorithm while ensuring it satisfies the safety constraint. Finally, we show in simulations that SaVeR produces low MSE policy evaluation while satisfying the safety constraint.

Optimal Design for Human Feedback

Learning of preference models from human feedback has been central to recent advances in artificial intelligence. Motivated by this progress, and the cost of obtaining high-quality human annotations, we study the problem of data collection for learning preference models. The key idea in our work is to generalize optimal designs, a tool for computing efficient data logging policies, to ranked lists. To show the generality of our ideas, we study both absolute and relative feedback on items in the list. We design efficient algorithms for both settings and analyze them. We prove that our preference model estimators improve with more data and so does the ranking error under the estimators. Finally, we experiment with several synthetic and real-world datasets to show the statistical efficiency of our algorithms.

Experimental Design for Active Transductive Inference in Large Language Models

Transduction, the ability to include query-specific examples in the prompt at inference time, is one of the emergent abilities of large language models (LLMs). In this work, we propose a framework for adaptive prompt design called active transductive inference (ATI). We design the LLM prompt by adaptively choosing few-shot examples for a given inference query. The examples are initially unlabeled and we query the user to label the most informative ones, which maximally reduces the uncertainty in the LLM prediction. We propose two algorithms, GO and SAL, which differ in how the few-shot examples are chosen. We analyze these algorithms in linear models: first GO and then use its equivalence with SAL. We experiment with many different tasks and show that GO and SAL outperform other methods for choosing few-shot examples in the LLM prompt at inference time.

Multi-task Representation Learning for Pure Exploration in Bilinear Bandits

We study multi-task representation learning for the problem of pure exploration in bilinear bandits. In bilinear bandits, an action takes the form of a pair of arms from two different entity types and the reward is a bilinear function of the known feature vectors of the arms. In the \textit{multi-task bilinear bandit problem}, we aim to find optimal actions for multiple tasks that share a common low-dimensional linear representation. The objective is to leverage this characteristic to expedite the process of identifying the best pair of arms for all tasks. We propose the algorithm GOBLIN that uses an experimental design approach to optimize sample allocations for learning the global representation as well as minimize the number of samples needed to identify the optimal pair of arms in individual tasks. To the best of our knowledge, this is the first study to give sample complexity analysis for pure exploration in bilinear bandits with shared representation. Our results demonstrate that by learning the shared representation across tasks, we achieve significantly improved sample complexity compared to the traditional approach of solving tasks independently.

Efficient and Interpretable Bandit Algorithms

Motivated by the importance of explainability in modern machine learning, we design bandit algorithms that are \emph{efficient} and \emph{interpretable}. A bandit algorithm is interpretable if it explores with the objective of reducing uncertainty in the unknown model parameter. To quantify the interpretability, we introduce a novel metric of \textit{uncertainty loss}, which compares the rate of the uncertainty reduction to the theoretical optimum. We propose CODE, a bandit algorithm based on a \textbf{C}onstrained \textbf{O}ptimal \textbf{DE}sign, that is interpretable and maximally reduces the uncertainty. The key idea in \code is to explore among all plausible actions, determined by a statistical constraint, to achieve interpretability. We implement CODE efficiently in both multi-armed and linear bandits and derive near-optimal regret bounds by leveraging the optimality criteria of the approximate optimal design. CODE can be also viewed as removing phases in conventional phased elimination, which makes it more practical and general. We demonstrate the advantage of \code by numerical experiments on both synthetic and real-world problems. CODE outperforms other state-of-the-art interpretable designs while matching the performance of popular but uninterpretable designs, such as upper confidence bound algorithms.

SPEED: Experimental Design for Policy Evaluation in Linear Heteroscedastic Bandits

In this paper, we study the problem of optimal data collection for policy evaluation in linear bandits. In policy evaluation, we are given a target policy and asked to estimate the expected cumulative reward it will obtain when executed in an environment formalized as a multi-armed bandit. In this paper, we focus on linear bandit setting with heteroscedastic reward noise. This is the first work that focuses on such an optimal data collection strategy for policy evaluation involving heteroscedastic reward noise in the linear bandit setting. We first formulate an optimal design for weighted least squares estimates in the heteroscedastic linear bandit setting that reduces the MSE of the target policy. We term this as policy-weighted least square estimation and use this formulation to derive the optimal behavior policy for data collection. We then propose a novel algorithm SPEED (Structured Policy Evaluation Experimental Design) that tracks the optimal behavior policy and derive its regret with respect to the optimal behavior policy. Finally, we empirically validate that SPEED leads to policy evaluation with mean squared error comparable to the oracle strategy and significantly lower than simply running the target policy.

Safety Aware Changepoint Detection for Piecewise i.i.d. Bandits

In this paper, we consider the setting of piecewise i.i.d. bandits under a safety constraint. In this piecewise i.i.d. setting, there exists a finite number of changepoints where the mean of some or all arms change simultaneously. We introduce the safety constraint studied in \citet{wu2016conservative} to this setting such that at any round the cumulative reward is above a constant factor of the default action reward. We propose two actively adaptive algorithms for this setting that satisfy the safety constraint, detect changepoints, and restart without the knowledge of the number of changepoints or their locations. We provide regret bounds for our algorithms and show that the bounds are comparable to their counterparts from the safe bandit and piecewise i.i.d. bandit literature. We also provide the first matching lower bounds for this setting. Empirically, we show that our safety-aware algorithms perform similarly to the state-of-the-art actively adaptive algorithms that do not satisfy the safety constraint.

ReVar: Strengthening Policy Evaluation via Reduced Variance Sampling

This paper studies the problem of data collection for policy evaluation in Markov decision processes (MDPs). In policy evaluation, we are given a target policy and asked to estimate the expected cumulative reward it will obtain in an environment formalized as an MDP. We develop theory for optimal data collection within the class of tree-structured MDPs by first deriving an oracle data collection strategy that uses knowledge of the variance of the reward distributions. We then introduce the Reduced Variance Sampling (ReVar) algorithm that approximates the oracle strategy when the reward variances are unknown a priori and bound its sub-optimality compared to the oracle strategy. Finally, we empirically validate that ReVar leads to policy evaluation with mean squared error comparable to the oracle strategy and significantly lower than simply running the target policy.