The main contributions of our works are theoretical. Thus, we obtain the following result: Theorem 3. There are several cases that we need to consider. Intuitively, if the user is recommended a golden item during the explore component, it is a good event in any case. We generate three synthetic datasets to validate our algorithms.

We study the problem of sampling from strongly log-concave distributions over $\mathbb{R}^d$ using the Poisson midpoint discretization (a variant of the randomized midpoint method) for overdamped/underdamped Langevin dynamics. We prove its convergence in the 2-Wasserstein distance ($W_2$), achieving a cubic speedup in dependence on the target accuracy ($ε$) over the Euler-Maruyama discretization, surpassing existing bounds for randomized midpoint methods. Notably, in the case of underdamped Langevin dynamics, we demonstrate the complexity of $W_2$ convergence is much smaller than the complexity lower bounds for convergence in $L^2$ strong error established in the literature.

Our goal in this section is twofold. To avoid excessive repetition of notation and proof arguments, we purposefully leave this section not self-contained and only outline these adjustments needed. We refer an interested reader to the work of Auer et al. We leave it to future work to optimize the dependence on N and K . In our MA-MAB problem, an algorithm is allowed to "pull" a distribution over the arms In the proof of their Lemma A.1, in the explanation of their Equation (30), they cite the assumption that given the rewards observed in the first Finally, in the proof of their Theorem A.2, they again consider the probability Thus, we have the following lower bound.

We study the problem of learning junta distributions on $\{0, 1\}^n$, where a distribution is a $k$-junta if its probability mass function depends on a subset of at most $k$ variables. We make two main contributions: - We show that learning $k$-junta distributions is \emph{computationally} equivalent to learning $k$-parity functions with noise (LPN), a landmark problem in computational learning theory. - We design an algorithm for learning junta distributions whose statistical complexity is optimal, up to polylogarithmic factors. Computationally, our algorithm matches the complexity of previous (non-sample-optimal) algorithms. Combined, our two contributions imply that our algorithm cannot be significantly improved, statistically or computationally, barring a breakthrough for LPN.

Deep learning algorithms have a large number of trainable parameters often with sizes of hundreds of thousands or more. Training this algorithm requires a large amount of training data and generating a sufficiently large dataset for these algorithms is costly\cite{noguchi2019image}. GANs are generative neural networks that use two deep learning networks that are competing with each other. The networks are generator and discriminator networks. The generator tries to generate realistic images which resemble the actual training dataset by approximating the training data distribution and the discriminator is trained to classify images as real or fake(generated)\cite{goodfellow2016nips}. Training these GAN algorithms also requires a large amount of training dataset\cite{noguchi2019image}. In this study, the aim is to address the question, "Given an unconditioned pretrained generator network and a pretrained classifier, is it feasible to develop a conditioned generator without relying on any training dataset?" The paper begins with a general introduction to the problem. The subsequent sections are structured as follows: Section 2 provides background information on the problem. Section 3 reviews relevant literature on the topic. Section 4 outlines the methodology employed in this study. Section 5 presents the experimental results. Section 6 discusses the findings and proposes potential future research directions. Finally, Section 7 offers concluding remarks. The implementation can be accessed \href{https://github.com/kidist-amde/BigGAN-PyTorch}{here}.

We study a federated linear bandits model, where $M$ clients communicate with a central server to solve a linear contextual bandits problem with finite adversarial action sets that may be different across clients. To address the unique challenges of adversarial finite action sets, we propose the FedSupLinUCB algorithm, which extends the principles of SupLinUCB and OFUL algorithms in linear contextual bandits. We prove that FedSupLinUCB achieves a total regret of $\tilde{O}(\sqrt{d T})$, where $T$ is the total number of arm pulls from all clients, and $d$ is the ambient dimension of the linear model. This matches the minimax lower bound and thus is order-optimal (up to polylog terms). We study both asynchronous and synchronous cases and show that the communication cost can be controlled as $O(d M^2 \log(d)\log(T))$ and $O(\sqrt{d^3 M^3} \log(d))$, respectively. The FedSupLinUCB design is further extended to two scenarios: (1) variance-adaptive, where a total regret of $\tilde{O} (\sqrt{d \sum \nolimits_{t=1}^{T} \sigma_t^2})$ can be achieved with $\sigma_t^2$ being the noise variance of round $t$; and (2) adversarial corruption, where a total regret of $\tilde{O}(\sqrt{dT} + d C_p)$ can be achieved with $C_p$ being the total corruption budget. Experiment results corroborate the theoretical analysis and demonstrate the effectiveness of FedSupLinUCB on both synthetic and real-world datasets.