Test-time adaptation is the problem of adapting a source pre-trained model using test inputs from a target domain without access to source domain data. Most of the existing approaches address the setting in which the target domain is stationary. Moreover, these approaches are prone to making erroneous predictions with unreliable uncertainty estimates when distribution shifts occur. Hence, test-time adaptation in the face of non-stationary target domain shift becomes a problem of significant interest. To address these issues, we propose a principled approach, PETAL (Probabilistic lifElong Test-time Adaptation with seLf-training prior), which looks into this problem from a probabilistic perspective using a partly data-dependent prior. A student-teacher framework, where the teacher model is an exponential moving average of the student model naturally emerges from this probabilistic perspective. In addition, the knowledge from the posterior distribution obtained for the source task acts as a regularizer. To handle catastrophic forgetting in the long term, we also propose a data-driven model parameter resetting mechanism based on the Fisher information matrix (FIM). Moreover, improvements in experimental results suggest that FIM based data-driven parameter restoration contributes to reducing the error accumulation and maintaining the knowledge of recent domain by restoring only the irrelevant parameters. In terms of predictive error rate as well as uncertainty based metrics such as Brier score and negative log-likelihood, our method achieves better results than the current state-of-the-art for online lifelong test time adaptation across various benchmarks, such as CIFAR-10C, CIFAR-100C, ImageNetC, and ImageNet3DCC datasets.

We consider the problem of off-policy evaluation (OPE) in reinforcement learning (RL), where the goal is to estimate the performance of an evaluation policy, $\pi_e$, using a fixed dataset, $\mathcal{D}$, collected by one or more policies that may be different from $\pi_e$. Current OPE algorithms may produce poor OPE estimates under policy distribution shift i.e., when the probability of a particular state-action pair occurring under $\pi_e$ is very different from the probability of that same pair occurring in $\mathcal{D}$ (Voloshin et al. 2021, Fu et al. 2021). In this work, we propose to improve the accuracy of OPE estimators by projecting the high-dimensional state-space into a low-dimensional state-space using concepts from the state abstraction literature. Specifically, we consider marginalized importance sampling (MIS) OPE algorithms which compute state-action distribution correction ratios to produce their OPE estimate. In the original ground state-space, these ratios may have high variance which may lead to high variance OPE. However, we prove that in the lower-dimensional abstract state-space the ratios can have lower variance resulting in lower variance OPE. We then highlight the challenges that arise when estimating the abstract ratios from data, identify sufficient conditions to overcome these issues, and present a minimax optimization problem whose solution yields these abstract ratios. Finally, our empirical evaluation on difficult, high-dimensional state-space OPE tasks shows that the abstract ratios can make MIS OPE estimators achieve lower mean-squared error and more robust to hyperparameter tuning than the ground ratios.

Finetuning language models on a collection of datasets phrased as instructions has been shown to improve model performance and generalization to unseen tasks. In this paper we explore instruction finetuning with a particular focus on (1) scaling the number of tasks, (2) scaling the model size, and (3) finetuning on chain-of-thought data. We find that instruction finetuning with the above aspects dramatically improves performance on a variety of model classes (PaLM, T5, U-PaLM), prompting setups (zero-shot, few-shot, CoT), and evaluation benchmarks (MMLU, BBH, TyDiQA, MGSM, open-ended generation). For instance, Flan-PaLM 540B instruction-finetuned on 1.8K tasks outperforms PALM 540B by a large margin (+9.4% on average). Flan-PaLM 540B achieves state-of-the-art performance on several benchmarks, such as 75.2% on five-shot MMLU. We also publicly release Flan-T5 checkpoints, which achieve strong few-shot performance even compared to much larger models, such as PaLM 62B. Overall, instruction finetuning is a general method for improving the performance and usability of pretrained language models.