Importance Sampling (IS) is a widely used building block for a large variety of off-policy estimation and learning algorithms. However, empirical and theoretical studies have progressively shown that vanilla IS leads to poor estimations whenever the behavioral and target policies are too dissimilar. In this paper, we analyze the theoretical properties of the IS estimator by deriving a novel anticoncentration bound that formalizes the intuition behind its undesired behavior. Then, we propose a new class of IS transformations, based on the notion of power mean. To the best of our knowledge, the resulting estimator is the first to achieve, under certain conditions, two key properties: (i) it displays a subgaussian concentration rate; (ii) it preserves the differentiability in the target distribution. Finally, we provide numerical simulations on both synthetic examples and contextual bandits, in comparison with off-policy evaluation and learning baselines.

Offline policy learning is aimed at learning decision-making policies using existing datasets of trajectories without collecting additional data. The primary motivation for using reinforcement learning (RL) instead of supervised learning techniques such as behavior cloning is to find a policy that achieves a higher average return than the trajectories constituting the dataset. However, we empirically find that when a dataset is dominated by suboptimal trajectories, state-of-the-art offline RL algorithms do not substantially improve over the average return of trajectories in the dataset. We argue this is due to an assumption made by current offline RL algorithms of staying close to the trajectories in the dataset. If the dataset primarily consists of sub-optimal trajectories, this assumption forces the policy to mimic the suboptimal actions. We overcome this issue by proposing a sampling strategy that enables the policy to only be constrained to "good data" rather than all actions in the dataset (i.e., uniform sampling). We present a realization of the sampling strategy and an algorithm that can be used as a plug-and-play module in standard offline RL algorithms. Our evaluation demonstrates significant performance gains in 72 imbalanced datasets, D4RL dataset, and across three different offline RL algorithms.

Importance Sampling (IS) is a method for approximating expectations under a target distribution using independent samples from a proposal distribution and the associated importance weights. In many applications, the target distribution is known only up to a normalization constant, in which case self-normalized IS (SNIS) can be used. While the use of self-normalization can have a positive effect on the dispersion of the estimator, it introduces bias. In this work, we propose a new method, BR-SNIS, whose complexity is essentially the same as that of SNIS and which significantly reduces bias without increasing the variance. This method is a wrapper in the sense that it uses the same proposal samples and importance weights as SNIS, but makes clever use of iterated sampling-importance resampling (i-SIR) to form a bias-reduced version of the estimator. We furnish the proposed algorithm with rigorous theoretical results, including new bias, variance and high-probability bounds, and these are illustrated by numerical examples.

The Multi-modal Large Language Model (MLLM) based Referring Expression Generation (REG) task has gained increasing popularity, which aims to generate an unambiguous text description that applies to exactly one object or region in the image by leveraging foundation models. We empirically found that there exists a potential trade-off between the detailedness and the correctness of the descriptions for the referring objects. On the one hand, generating sentences with more details is usually required in order to provide more precise object descriptions. On the other hand, complicated sentences could easily increase the probability of hallucinations. To address this issue, we propose a training-free framework, named ``unleash-then-eliminate'', which first elicits the latent information in the intermediate layers, and then adopts a cycle-consistency-based decoding method to alleviate the production of hallucinations. Furthermore, to reduce the computational load of cycle-consistency-based decoding, we devise a Probing-based Importance Estimation method to statistically estimate the importance weights of intermediate layers within a subset. These importance weights are then incorporated into the decoding process over the entire dataset, intervening in the next token prediction from intermediate layers.Extensive experiments conducted on the RefCOCOg and PHD benchmarks show that our proposed framework could outperform existing methods on both semantic and hallucination-related metrics.

Variational inference with α-divergences has been widely used in modern probabilistic machine learning. Compared to Kullback-Leibler (KL) divergence, a major advantage of using α-divergences (with positive α values) is their mass-covering property. However, estimating and optimizing α-divergences require to use importance sampling, which could have extremely large or infinite variances due to heavy tails of importance weights. In this paper, we propose a new class of tail-adaptive f-divergences that adaptively change the convex function f with the tail of the importance weights, in a way that theoretically guarantee finite moments, while simultaneously achieving mass-covering properties. We test our methods on Bayesian neural networks, as well as deep reinforcement learning in which our method is applied to improve a recent soft actor-critic (SAC) algorithm (Haarnoja et al., 2018). Our results show that our approach yields significant advantages compared with existing methods based on classical KL and α-divergences.

Training a policy in a source domain for deployment in the target domain under a dynamics shift can be challenging, often resulting in performance degradation.