Language model alignment methods, such as reinforcement learning from human feedback (RLHF), have led to impressive advances in language model capabilities, but existing techniques are limited by a widely observed phenomenon known as overoptimization, where the quality of the language model plateaus or degrades over the course of the alignment process. Overoptimization is often attributed to overfitting to an inaccurate reward model, and while it can be mitigated through online data collection, this is infeasible in many settings. This raises a fundamental question: Do existing offline alignment algorithms make the most of the data they have, or can their sample-efficiency be improved further? We address this question with a new algorithm for offline alignment, $\chi^2$-Preference Optimization ($\chi$PO). $\chi$PO is a one-line change to Direct Preference Optimization (DPO; Rafailov et al., 2023), which only involves modifying the logarithmic link function in the DPO objective. Despite this minimal change, $\chi$PO implicitly implements the principle of pessimism in the face of uncertainty via regularization with the $\chi^2$-divergence -- which quantifies uncertainty more effectively than KL-regularization -- and provably alleviates overoptimization, achieving sample-complexity guarantees based on single-policy concentrability -- the gold standard in offline reinforcement learning. $\chi$PO's simplicity and strong guarantees make it the first practical and general-purpose offline alignment algorithm that is provably robust to overoptimization.

In machine learning models, the estimation of errors is often complex due to distribution bias, particularly in spatial data such as those found in environmental studies. We introduce an approach based on the ideas of importance sampling to obtain an unbiased estimate of the target error. By taking into account difference between desirable error and available data, our method reweights errors at each sample point and neutralizes the shift. Importance sampling technique and kernel density estimation were used for reweighteing. We validate the effectiveness of our approach using artificial data that resemble real-world spatial datasets. Our findings demonstrate advantages of the proposed approach for the estimation of the target error, offering a solution to a distribution shift problem. Overall error of predictions dropped from 7% to just 2% and it gets smaller for larger samples.

Interference is a ubiquitous problem in experiments conducted on two-sided content marketplaces, such as Douyin (China's analog of TikTok). In many cases, creators are the natural unit of experimentation, but creators interfere with each other through competition for viewers' limited time and attention. "Naive" estimators currently used in practice simply ignore the interference, but in doing so incur bias on the order of the treatment effect. We formalize the problem of inference in such experiments as one of policy evaluation. Off-policy estimators, while unbiased, are impractically high variance. We introduce a novel Monte-Carlo estimator, based on "Differences-in-Qs" (DQ) techniques, which achieves bias that is second-order in the treatment effect, while remaining sample-efficient to estimate. On the theoretical side, our contribution is to develop a generalized theory of Taylor expansions for policy evaluation, which extends DQ theory to all major MDP formulations. On the practical side, we implement our estimator on Douyin's experimentation platform, and in the process develop DQ into a truly "plug-and-play" estimator for interference in real-world settings: one which provides robust, low-bias, low-variance treatment effect estimates; admits computationally cheap, asymptotically exact uncertainty quantification; and reduces MSE by 99\% compared to the best existing alternatives in our applications.

We propose UCBMQ, Upper Confidence Bound Momentum Q-learning, a new algorithm for reinforcement learning in tabular and possibly stage-dependent, episodic Markov decision process. UCBMQ is based on Q-learning where we add a momentum term and rely on the principle of optimism in face of uncertainty to deal with exploration. Our new technical ingredient of UCBMQ is the use of momentum to correct the bias that Q-learning suffers while, at the same time, limiting the impact it has on the second-order term of the regret. For UCBMQ , we are able to guarantee a regret of at most $O(\sqrt{H^3SAT}+ H^4 S A )$ where $H$ is the length of an episode, $S$ the number of states, $A$ the number of actions, $T$ the number of episodes and ignoring terms in poly$log(SAHT)$. Notably, UCBMQ is the first algorithm that simultaneously matches the lower bound of $\Omega(\sqrt{H^3SAT})$ for large enough $T$ and has a second-order term (with respect to the horizon $T$) that scales only linearly with the number of states $S$.

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