In real-world project scheduling applications, activity durations are often uncertain. Proactive scheduling can effectively cope with the duration uncertainties, by generating robust baseline solutions according to a priori stochastic knowledge. However, most of the existing proactive approaches assume that the duration uncertainty of an activity is not related to its scheduled start time, which may not hold in many real-world scenarios. In this paper, we relax this assumption by allowing the duration uncertainty to be time-dependent, which is caused by the uncertainty of whether the activity can be executed on each time slot. We propose a stochastic optimization model to find an optimal Partial-order Schedule (POS) that minimizes the expected makespan. This model can cover both the time-dependent uncertainty studied in this paper and the traditional time-independent duration uncertainty. To circumvent the underlying complexity in evaluating a given solution, we approximate the stochastic optimization model based on Sample Average Approximation (SAA). Finally, we design two efficient branch-and-bound algorithms to solve the NP-hard SAA problem. Empirical evaluation confirms that our approach can generate high-quality proactive solutions for a variety of uncertainty distributions.

Finding hard instances, which need a long time to solve, of graph problems such as the graph coloring problem and the maximum clique problem, is important for (1) building a good benchmark for evaluating the performance of algorithms, and (2) analyzing the algorithms to accelerate them. The existing methods for generating hard instances rely on parameters or rules that are found by domain experts; however, they are specific to the problem. Hence, it is difficult to generate hard instances for general cases. To address this issue, in this paper, we formulate finding hard instances of graph problems as two equivalent optimization problems. Then, we propose a method to automatically find hard instances by solving the optimization problems. The advantage of the proposed algorithm over the existing rule based approach is that it does not require any task specific knowledge. To the best of our knowledge, this is the first non-trivial method in the literature to automatically find hard instances. Through experiments on various problems, we demonstrate that our proposed method can generate instances that are a few to several orders of magnitude harder than the random based approach in many settings. In particular, our method outperforms rule-based algorithms in the 3-coloring problem.

Minimax, as the name suggest, is a method in decision theory for minimizing the maximum loss. Alternatively, it can be thought of as maximizing the minimum gain, which is also know as Maximin. It all started from a two player zero-sum game theory, covering both the cases where players take alternate moves and those where they made simultaneous moves. It has also been extended to more complex games and to general decision making in the presence of uncertainty. In the above explanation, it has been mentioned that the minimax algorithms started off with the concept of zero-sum.

Minimax, as the name suggest, is a method in decision theory for minimizing the maximum loss.

Google remains at the forefront of developments in many areas that have the potential to disrupt local search. Artificial intelligence (AI), virtual reality (VR), the internet of things (IoT), voice search and cloud technology are all being increasingly used by consumers and businesses alike. Yet there is one area where Google doesn't sit in pole position: social media. Google has made several attempts to get some traction in social media: Orkut, Dodgeball, Buzz, Latitude. The fact that you likely don't recognize these names says enough about their success.

Comparing different algorithms is hard. For almost any pair of algorithms and measure of algorithm performance like running time or solution quality, each algorithm will perform better than the other on some inputs.a For example, the insertion sort algorithm is faster than merge sort on already-sorted arrays but slower on many other inputs. When two algorithms have incomparable performance, how can we deem one of them "better than" the other? Worst-case analysis is a specific modeling choice in the analysis of algorithms, where the overall performance of an algorithm is summarized by its worst performance on any input of a given size. The "better" algorithm is then the one with superior worst-case performance. Merge sort, with its worst-case asymptotic running time of Θ(n log n) for arrays of length n, is better in this sense than insertion sort, which has a worst-case running time of Θ(n2). While crude, worst-case analysis can be tremendously useful, and it is the dominant paradigm for algorithm analysis in theoretical computer science. A good worst-case guarantee is the best-case scenario for an algorithm, certifying its general-purpose utility and absolving its users from understanding which inputs are relevant to their applications. Remarkably, for many fundamental computational problems, there are algorithms with excellent worst-case performance guarantees. The lion's share of an undergraduate algorithms course comprises algorithms that run in linear or near-linear time in the worst case.

We derive an optimal policy for adaptively restarting a randomized algorithm, based on observed features of the run-so-far, so as to minimize the expected time required for the algorithm to successfully terminate. Given a suitable Bayesian prior, this result can be used to select the optimal black-box optimization algorithm from among a large family of algorithms that includes random search, Successive Halving, and Hyperband. On CIFAR-10 and ImageNet hyperparameter tuning problems, the proposed policies offer up to a factor of 13 improvement over random search in terms of expected time to reach a given target accuracy, and up to a factor of 3 improvement over a baseline adaptive policy that terminates a run whenever its accuracy is below-median.

Neural Architecture Search (NAS) aims to facilitate the design of deep networks for new tasks. Existing techniques rely on two stages: searching over the architecture space and validating the best architecture. Evaluating NAS algorithms is currently solely done by comparing their results on the downstream task. While intuitive, this fails to explicitly evaluate the effectiveness of their search strategies. In this paper, we extend the NAS evaluation procedure to include the search phase. To this end, we compare the quality of the solutions obtained by NAS search policies with that of random architecture selection. We find that: (i) On average, the random policy outperforms state-of-the-art NAS algorithms; and (ii) The results and candidate rankings of NAS algorithms do not reflect the true performance of the candidate architectures. While our former finding illustrates the fact that the NAS search space has been sufficiently constrained so that random solutions yield good results, we trace the latter back to the weight sharing strategy used by state-of-the-art NAS methods. In contrast with common belief, weight sharing negatively impacts the training of good architectures, thus reducing the effectiveness of the search process. We believe that following our evaluation framework will be key to designing NAS strategies that truly discover superior architectures.

Neural architecture search (NAS) is a promising research direction that has the potential to replace expert-designed networks with learned, task-specific architectures. In this work, in order to help ground the empirical results in this field, we propose new NAS baselines that build off the following observations: (i) NAS is a specialized hyperparameter optimization problem; and (ii) random search is a competitive baseline for hyperparameter optimization. Leveraging these observations, we evaluate both random search with early-stopping and a novel random search with weight-sharing algorithm on two standard NAS benchmarks---PTB and CIFAR-10. Our results show that random search with early-stopping is a competitive NAS baseline, e.g., it performs at least as well as ENAS, a leading NAS method, on both benchmarks. Additionally, random search with weight-sharing outperforms random search with early-stopping, achieving a state-of-the-art NAS result on PTB and a highly competitive result on CIFAR-10. Finally, we explore the existing reproducibility issues of published NAS results. We note the lack of source material needed to exactly reproduce these results, and further discuss the robustness of published results given the various sources of variability in NAS experimental setups. Relatedly, we provide all information (code, random seeds, documentation) needed to exactly reproduce our results, and report our random search with weight-sharing results for each benchmark on two independent experimental runs.

We demonstrate the first possibility of a sub-linear memory sketch for solving the approximate near-neighbor search problem. In particular, we develop an online sketching algorithm that can compress $N$ vectors into a tiny sketch consisting of small arrays of counters whose size scales as $O(N^{b}\log^2{N})$, where $b < 1$ depending on the stability of the near-neighbor search. This sketch is sufficient to identify the top-$v$ near-neighbors with high probability. To the best of our knowledge, this is the first near-neighbor search algorithm that breaks the linear memory ($O(N)$) barrier. We achieve sub-linear memory by combining advances in locality sensitive hashing (LSH) based estimation, especially the recently-published ACE algorithm, with compressed sensing and heavy hitter techniques. We provide strong theoretical guarantees; in particular, our analysis sheds new light on the memory-accuracy tradeoff in the near-neighbor search setting and the role of sparsity in compressed sensing, which could be of independent interest. We rigorously evaluate our framework, which we call RACE (Repeated ACE) data structures on a friend recommendation task on the Google plus graph with more than 100,000 high-dimensional vectors. RACE provides compression that is orders of magnitude better than the random projection based alternative, which is unsurprising given the theoretical advantage. We anticipate that RACE will enable both new theoretical perspectives on near-neighbor search and new methodologies for applications like high-speed data mining, internet-of-things (IoT), and beyond.