Smooth functions on graphs have wide applications in manifold and semi-supervised learning. In this paper, we study a bandit problem where the payoffs of arms are smooth on a graph. This framework is suitable for solving online learning problems that involve graphs, such as content-based recommendation. In this problem, each item we can recommend is a node and its expected rating is similar to its neighbors. The goal is to recommend items that have high expected ratings. We aim for the algorithms where the cumulative regret with respect to the optimal policy would not scale poorly with the number of nodes. In particular, we introduce the notion of an effective dimension, which is small in real-world graphs, and propose two algorithms for solving our problem that scale linearly and sublinearly in this dimension. Our experiments on real-world content recommendation problem show that a good estimator of user preferences for thousands of items can be learned from just tens of nodes evaluations.

We propose a simple detection mechanism for the Gumbel watermarking scheme proposed by Aaronson (2022). The new mechanism is proven to be near-optimal in a problem-dependent sense among all model-agnostic watermarking schemes under the assumption that the next-token distribution is sampled i.i.d.

Let k (,) be the ν = 2 .5 Matérn kernel.

The "folk wisdom" in the literature is that the focus on local optimization sidesteps the curse of dimensionality;

The main result is presented in Theorem 2. According to the definition of the Fiedler vector, we have ( L + L)( f + f) = ( λ + λ)( f + f). We outline the proof below for interested readers. The main result is presented in Theorem 2. We first present Stewart's theorem in Lemma 1 to assist Actual times may differ depending on hardware and environment. We also show the number of model parameters required for each method in Table S3. Hyper-parameters were selected based on a coarse search on the validation set.

Achieving a balance between image quality (precision) and diversity (recall) is a significant challenge in the domain of generative models.

Inthis paper, to overcome these limitations, we propose a new algorithm based on the principle ofoptimism inthefaceofuncertainty.

If used for optimization,E(θ) is the function we are interested in minimizing.

Designing efficient reinforcement learning (RL) algorithms for environments with large state and action spaces is one of the main tasks in the RL community.