Predictive Performance Comparison of Decision Policies Under Confounding

Predictive models are often introduced to decision-making tasks under the rationale that they improve performance over an existing decision-making policy. However, it is challenging to compare predictive performance against an existing decision-making policy that is generally under-specified and dependent on unobservable factors. These sources of uncertainty are often addressed in practice by making strong assumptions about the data-generating mechanism. In this work, we propose a method to compare the predictive performance of decision policies under a variety of modern identification approaches from the causal inference and off-policy evaluation literatures (e.g., instrumental variable, marginal sensitivity model, proximal variable). Key to our method is the insight that there are regions of uncertainty that we can safely ignore in the policy comparison. We develop a practical approach for finite-sample estimation of regret intervals under no assumptions on the parametric form of the status quo policy. We verify our framework theoretically and via synthetic data experiments. We conclude with a real-world application using our framework to support a pre-deployment evaluation of a proposed modification to a healthcare enrollment policy.

Provable Multi-Party Reinforcement Learning with Diverse Human Feedback

Reinforcement learning with human feedback (RLHF) is an emerging paradigm to align models with human preferences. Typically, RLHF aggregates preferences from multiple individuals who have diverse viewpoints that may conflict with each other. Our work \textit{initiates} the theoretical study of multi-party RLHF that explicitly models the diverse preferences of multiple individuals. We show how traditional RLHF approaches can fail since learning a single reward function cannot capture and balance the preferences of multiple individuals. To overcome such limitations, we incorporate meta-learning to learn multiple preferences and adopt different social welfare functions to aggregate the preferences across multiple parties. We focus on the offline learning setting and establish sample complexity bounds, along with efficiency and fairness guarantees, for optimizing diverse social welfare functions such as Nash, Utilitarian, and Leximin welfare functions. Our results show a separation between the sample complexities of multi-party RLHF and traditional single-party RLHF. Furthermore, we consider a reward-free setting, where each individual's preference is no longer consistent with a reward model, and give pessimistic variants of the von Neumann Winner based on offline preference data. Taken together, our work showcases the advantage of multi-party RLHF but also highlights its more demanding statistical complexity.

Regret Minimization in Stackelberg Games with Side Information

In its most basic form, a Stackelberg game is a two-player game in which a leader commits to a (mixed) strategy, and a follower best-responds. Stackelberg games are perhaps one of the biggest success stories of algorithmic game theory over the last decade, as algorithms for playing in Stackelberg games have been deployed in many real-world domains including airport security, anti-poaching efforts, and cyber-crime prevention. However, these algorithms often fail to take into consideration the additional information available to each player (e.g. traffic patterns, weather conditions, network congestion), a salient feature of reality which may significantly affect both players' optimal strategies. We formalize such settings as Stackelberg games with side information, in which both players observe an external context before playing. The leader then commits to a (possibly context-dependent) strategy, and the follower best-responds to both the leader's strategy and the context. We focus on the online setting in which a sequence of followers arrive over time, and the context may change from round-to-round. In sharp contrast to the non-contextual version, we show that it is impossible for the leader to achieve good performance (measured by regret) in the full adversarial setting (i.e., when both the context and the follower are chosen by an adversary). However, it turns out that a little bit of randomness goes a long way. Motivated by our impossibility result, we show that no-regret learning is possible in two natural relaxations: the setting in which the sequence of followers is chosen stochastically and the sequence of contexts is adversarial, and the setting in which the sequence of contexts is stochastic and the sequence of followers is chosen by an adversary.

Hybrid Inverse Reinforcement Learning

The inverse reinforcement learning approach to imitation learning is a double-edged sword. On the one hand, it can enable learning from a smaller number of expert demonstrations with more robustness to error compounding than behavioral cloning approaches. On the other hand, it requires that the learner repeatedly solve a computationally expensive reinforcement learning (RL) problem. Often, much of this computation is wasted searching over policies very dissimilar to the expert's. In this work, we propose using hybrid RL -- training on a mixture of online and expert data -- to curtail unnecessary exploration. Intuitively, the expert data focuses the learner on good states during training, which reduces the amount of exploration required to compute a strong policy. Notably, such an approach doesn't need the ability to reset the learner to arbitrary states in the environment, a requirement of prior work in efficient inverse RL. More formally, we derive a reduction from inverse RL to expert-competitive RL (rather than globally optimal RL) that allows us to dramatically reduce interaction during the inner policy search loop while maintaining the benefits of the IRL approach. This allows us to derive both model-free and model-based hybrid inverse RL algorithms with strong policy performance guarantees. Empirically, we find that our approaches are significantly more sample efficient than standard inverse RL and several other baselines on a suite of continuous control tasks.

The Virtues of Pessimism in Inverse Reinforcement Learning

Inverse Reinforcement Learning (IRL) is a powerful framework for learning complex behaviors from expert demonstrations. However, it traditionally requires repeatedly solving a computationally expensive reinforcement learning (RL) problem in its inner loop. It is desirable to reduce the exploration burden by leveraging expert demonstrations in the inner-loop RL. As an example, recent work resets the learner to expert states in order to inform the learner of high-reward expert states. However, such an approach is infeasible in the real world. In this work, we consider an alternative approach to speeding up the RL subroutine in IRL: \emph{pessimism}, i.e., staying close to the expert's data distribution, instantiated via the use of offline RL algorithms. We formalize a connection between offline RL and IRL, enabling us to use an arbitrary offline RL algorithm to improve the sample efficiency of IRL. We validate our theory experimentally by demonstrating a strong correlation between the efficacy of an offline RL algorithm and how well it works as part of an IRL procedure. By using a strong offline RL algorithm as part of an IRL procedure, we are able to find policies that match expert performance significantly more efficiently than the prior art.

Leveraging Public Representations for Private Transfer Learning

Motivated by the recent empirical success of incorporating public data into differentially private learning, we theoretically investigate how a shared representation learned from public data can improve private learning. We explore two common scenarios of transfer learning for linear regression, both of which assume the public and private tasks (regression vectors) share a low-rank subspace in a high-dimensional space. In the first single-task transfer scenario, the goal is to learn a single model shared across all users, each corresponding to a row in a dataset. We provide matching upper and lower bounds showing that our algorithm achieves the optimal excess risk within a natural class of algorithms that search for the linear model within the given subspace estimate. In the second scenario of multitask model personalization, we show that with sufficient public data, users can avoid private coordination, as purely local learning within the given subspace achieves the same utility. Taken together, our results help to characterize the benefits of public data across common regimes of private transfer learning.

A Minimaximalist Approach to Reinforcement Learning from Human Feedback

We present Self-Play Preference Optimization (SPO), an algorithm for reinforcement learning from human feedback. Our approach is minimalist in that it does not require training a reward model nor unstable adversarial training and is therefore rather simple to implement. Our approach is maximalist in that it provably handles non-Markovian, intransitive, and stochastic preferences while being robust to the compounding errors that plague offline approaches to sequential prediction. To achieve the preceding qualities, we build upon the concept of a Minimax Winner (MW), a notion of preference aggregation from the social choice theory literature that frames learning from preferences as a zero-sum game between two policies. By leveraging the symmetry of this game, we prove that rather than using the traditional technique of dueling two policies to compute the MW, we can simply have a single agent play against itself while maintaining strong convergence guarantees. Practically, this corresponds to sampling multiple trajectories from a policy, asking a rater or preference model to compare them, and then using the proportion of wins as the reward for a particular trajectory. We demonstrate that on a suite of continuous control tasks, we are able to learn significantly more efficiently than reward-model based approaches while maintaining robustness to the intransitive and stochastic preferences that frequently occur in practice when aggregating human judgments.

Incentive-Aware Synthetic Control: Accurate Counterfactual Estimation via Incentivized Exploration

We consider a panel data setting in which one observes measurements of units over time, under different interventions. Our focus is on the canonical family of synthetic control methods (SCMs) which, after a pre-intervention time period when all units are under control, estimate counterfactual outcomes for test units in the post-intervention time period under control by using data from donor units who have remained under control for the entire post-intervention period. In order for the counterfactual estimate produced by synthetic control for a test unit to be accurate, there must be sufficient overlap between the outcomes of the donor units and the outcomes of the test unit. As a result, a canonical assumption in the literature on SCMs is that the outcomes for the test units lie within either the convex hull or the linear span of the outcomes for the donor units. However despite their ubiquity, such overlap assumptions may not always hold, as is the case when, e.g., units select their own interventions and different subpopulations of units prefer different interventions a priori. We shed light on this typically overlooked assumption, and we address this issue by incentivizing units with different preferences to take interventions they would not normally consider. Specifically, we provide a SCM for incentivizing exploration in panel data settings which provides incentive-compatible intervention recommendations to units by leveraging tools from information design and online learning. Using our algorithm, we show how to obtain valid counterfactual estimates using SCMs without the need for an explicit overlap assumption on the unit outcomes.