We study the reinforcement learning problem for discounted Markov Decision Processes (MDPs) under the tabular setting. We propose a model-based algorithm named UCBVI-γ, which is based on the optimism in the face of uncertainty principle and the Bernstein-type bonus.

Based on Minkowski's inequality for sums [2] with order 2: Using Eq. 1 and 3, Eq. 4 can be proved. Using Eq. 3, 10, and 2, we have the following distance(o Eq. 6 can be proved. Similar to proof in C, Theorem 4 can be proved. Theorem 1, 2 and Theorem 3, 4 can be generalized to Minkowski distance with order q, q > 1. Using Eq. 11 and 3, Eq. 4 can be proved.

Deep learning classifiers are assisting humans in making decisions and hence the user's trust in these models is of paramount importance. Trust is often a function of constant behavior. From an AI model perspective it means given the same input the user would expect the same output, especially for correct outputs, or in other words consistently correct outputs. This paper studies a model behavior in the context of periodic retraining of deployed models where the outputs from successive generations of the models might not agree on the correct labels assigned to the same input. We formally define consistency and correct-consistency of a learning model. We prove that consistency and correct-consistency of an ensemble learner is not less than the average consistency and correct-consistency of individual learners and correct-consistency can be improved with a probability by combining learners with accuracy not less than the average accuracy of ensemble component learners. To validate the theory using three datasets and two state-ofthe-art deep learning classifiers we also propose an efficient dynamic snapshot ensemble method and demonstrate its value.

The guidance scale of the diffusion model is set as 2.0, and the sampling step is 50. For synthetic pre-training, we adopt exactly the same training protocols as real images. Then, during fine-tuning, the base learning rate is decayed to be half of the normal learning rate. Since our whole model parameters are pre-trained with synthetic images, the fine-tuning learning rate is the same throughout the whole model. The model is pre-trained and fine-tuned for the same iterations as real images.

In the fixed budget thresholding bandit problem, an algorithm sequentially allocates a budgeted number of samples to different distributions. It then predicts whether the mean of each distribution is larger or lower than a given threshold. We introduce a large family of algorithms (containing most existing relevant ones), inspired by the Frank-Wolfe algorithm, and provide a thorough yet generic analysis of their performance. This allowed us to construct new explicit algorithms, for a broad class of problems, whose losses are within a small constant factor of the non-adaptive oracle ones. Quite interestingly, we observed that adaptive methods empirically greatly out-perform non-adaptive oracles, an uncommon behavior in standard online learning settings, such as regret minimization. We explain this surprising phenomenon on an insightful toy problem.

Robust Markov decision processes (MDPs) aim to handle changing or partially known system dynamics. To solve them, one typically resorts to robust optimization methods. However, this significantly increases computational complexity and limits scalability in both learning and planning.

We give a model of how to infer natural language rules by doing experiments.