Appendix The appendix is organized as follows. We also provide details of the annotation/calibration process and the baseline neural networks (NNs) in Section D and E, respectively. We discuss results regarding each weather condition and consideration of the K-Radar dataset as a pre-training dataset for other Radar tensor datasets in Section F and G, respectively. Finally, we introduce details of devkits and list relevant URLs to help with understanding the content of the paper in Section H and I, respectively. A.1 Additional samples of the K-Radar dataset and explanation of LPCs for each weather condition In the sleet (Figure 8-(e)) or heavy snow (Figure 8-(g)) condition, the Lidar point cloud (LPC) measurements of some objects ahead are lost when the ego-vehicle is driving.

Throughout the paper, we assume the'stack of rewards model' from chapter 4.6 of [60]. Since A7 A 1 is continuous on the space of invertible matrices, the result follows by the continuous mapping theorem. Lemma 2 Consider the setup from Part II of the proof of Proposition 2. Define ˆθn,t = Σn,t Pt 1 i=1 1 {a?i = ai = a(j)}wn,i, S?t(j) St(j) 0 is the number of'a(j) mistakes', and is associated with positive regret when the inequality is strict. Observe that we must have t 1(S?t(j) St(j)) 0 in probability, as otherwise there would be c, > 0 such that lim sup P(t 1(S?t(j) St(j)) >) >c, implying lim sup T 1 E[R2sT ] lim sup T 1 E[RNT] lim sup E T > c>0, which contradicts the assumption lim sup T 1 E[R2sT ] 0 (recall = mini ri >0). Finally, t 1(S?t(j) St(j)) 0 implies Since an analogous argument can be made for the covariance term, and A7 A 1 is continuous on the space of invertible matrices, ˆθn,t θ?n in probability by the continuous mapping theorem, as desired.

Owner of US tech giant reveals breach of one of world's most powerful AI models. Reports of unauthorised access to one of the most powerful Artificial Intelligence models yet developed have emerged. Nothing malicious, say the owners - but it has intensified focus on such technology falling into the wrong hands. So, how is AI being controlled globally? Will complex EU loan deal intensify conflict?

There has been recent interest in using machine-learned predictions to improve the worst-case guarantees of online algorithms. In this paper we continue this line of work by studying the online knapsack problem, but with very weak predictions: in the form of knowing an upper and lower bound for the number of items of each value. We systematically derive online algorithms that attain the best possible competitive ratio for any fixed prediction; we also extend the results to more general settings such as generalized one-way trading and two-stage online knapsack. Our work shows that even seemingly weak predictions can be utilized effectively to provably improve the performance of online algorithms.

The contributions of the authors are as follows. Luis Pineda led the engineering of the project, developed and implemented the core API, differentiable nonlinear solvers, motion planning example and tutorials, standard and autodiff cost functions, and backward mode experiments, coordinated with sub-teams to help design, implement, integrate and review of all aspects of the code and evaluations, wrote the paper.

We restate the theoretical statements and the algorithms here for completeness and convenience. Given a normalized monotone submodular function f:2 V! The objective aims to find the partition such that the minimum-valued block in the partition is maximized. For a ground set V and its elements (v1,v2,...,v n) coming in an arbitrary streaming order, the output solution of Alg. 1 has The output solution of Alg. 2 has We construct a set cover function as the tight example for Corollary 1. We illustrate the set cover function graphically in Figure 1. The circles are the areas to cover for the set cover function and the green inner circles and the red triangles are elements in the ground set (the outer yellow circles are not elements). The inner circles (green) largely overlap with the outer circles (yellow).