AIs can surpass human performance by a large margin.

We further evaluate SGBS+EAS on nine real-world based instance sets from [15]. Each instance set consists of 20 instances that have similar characteristics (i.e., they have been sampled from the same underlying distribution). The instance sets differ significantly in terms of several structural properties, for example, the number of customers n and their position (e.g., clustered vs. random positions). A more detailed description of instance sets can be found in [15]. One major advantage of neural combinatorial optimization approaches over traditional handcrafted optimization methods is their ability to quickly learn customized heuristics for new problem settings.

Algorithm 1 demonstrates the step-by-step operations of our beam search algorithm (see Sec. 4.3). We consider recovering sentences in the current work. We leave recovering longer paragraphs as future work. We keep 2000 examples of each dataset as the evaluation set, and use the left for training. "End-to-End optimization", "Reg" means the inclusion of a regularization term, "DR" refers to a discrete token Our approach is unique as it does not rely on end-to-end optimization, is demonstrated on large batch sizes (i.e.

Adversarial online learning is a well-studied framework for sequential decision making with numerous applications.

Furthermore, we illustrate various cases (e.g.,

We consider the problem of online regret minimization in linear bandits with access to prior observations (offline data) from the underlying bandit model. There are numerous applications where extensive offline data is often available, such as in recommendation systems, online advertising. Consequently, this problem has been studied intensively in recent literature. Our algorithm, Offline-Online Phased Elimination (OOPE), effectively incorporates the offline data to substantially reduce the online regret compared to prior work. To leverage offline information prudently, OOPE uses an extended D-optimal design within each exploration phase. OOPE achieves an online regret is $\tilde{O}(\sqrt{\deff T \log \left(|\mathcal{A}|T\right)}+d^2)$. $\deff \leq d)$ is the effective problem dimension which measures the number of poorly explored directions in offline data and depends on the eigen-spectrum $(λ_k)_{k \in [d]}$ of the Gram matrix of the offline data. The eigen-spectrum $(λ_k)_{k \in [d]}$ is a quantitative measure of the \emph{quality} of offline data. If the offline data is poorly explored ($\deff \approx d$), we recover the established regret bounds for purely online setting while, when offline data is abundant ($\Toff >> T$) and well-explored ($\deff = o(1) $), the online regret reduces substantially. Additionally, we provide the first known minimax regret lower bounds in this setting that depend explicitly on the quality of the offline data. These lower bounds establish the optimality of our algorithm in regimes where offline data is either well-explored or poorly explored. Finally, by using a Frank-Wolfe approximation to the extended optimal design we further improve the $O(d^{2})$ term to $O\left(\frac{d^{2}}{\deff} \min \{ \deff,1\} \right)$, which can be substantial in high dimensions with moderate quality of offline data $\deff = Ω(1)$.