Smooth game optimization has recently attracted great interest in machine learning as it generalizes the single-objective optimization paradigm. However, game dynamics is more complex due to the interaction between different players and is therefore fundamentally different from minimization, posing new challenges for algorithm design. Notably, it has been shown that negative momentum is preferred due to its ability to reduce oscillation in game dynamics. Nevertheless, existing analysis about negative momentum was restricted to simple bilinear games. In this paper, we extend the analysis to smooth and strongly-convex strongly-concave minimax games by taking the variational inequality formulation. By connecting momentum method with Chebyshev polynomials, we show that negative momentum accelerates convergence of game dynamics locally, though with a suboptimal rate. To the best of our knowledge, this is the \emph{first work} that provides an explicit convergence rate for negative momentum in this setting.

The use of deep learning techniques has achieved significant progress for program synthesis from input-output examples. However, when the program semantics become more complex, it still remains a challenge to synthesize programs that are consistent with the specification. In this work, we propose SED, a neural program generation framework that incorporates synthesis, execution, and debugging stages. Instead of purely relying on the neural program synthesizer to generate the final program, SED first produces initial programs using the neural program synthesizer component, then utilizes a neural program debugger to iteratively repair the generated programs. The integration of the debugger component enables SED to modify the programs based on the execution results and specification, which resembles the coding process of human programmers. On Karel, a challenging input-output program synthesis benchmark, SED reduces the error rate of the neural program synthesizer itself by a considerable margin, and outperforms the standard beam search for decoding.

Modern reinforcement learning and planning algorithms have achieved tremendous successes on various tasks [Mnih et al., 2015, Silver et al., 2017]. However, most of these algorithms work in the standard Markov decision process (MDP) framework where the goal is to maximize the cumulative reward and thus it can be difficult to apply them to various practical sequential decision-making problems. In this paper, we study planning in generalized MDPs, where instead of maximizing the cumulative reward, the goal is to maximize the objective value induced by a submodular function. To motivate our approach, let us consider the following scenario: a company manufactures cars, and as part of its customer service, continuously monitors the status of all cars produced by the company. Each car is equipped with a number of sensors, each of which constantly produces noisy measurements of some attribute of the car, e.g., speed, location, temperature, etc. Due to bandwidth constraints, at any moment, each car may choose to transmit data generated by a single sensor to the company. The goal is to combine the statistics collected over a fixed period of time, presumably from multiple sensors, to gather as much information about the car as possible. Perhaps one seemingly natural strategy is to transmit only data generated by the most "informative" sensor. However, as the output of a sensor remains the same between two samples, it is pointless to transmit the same data multiple times. One may alternatively try to order sensors by their "informativity" and always choose the most informative sensor that has not yet transmitted data since the last sample was generated.

In this article, a novel approach to solve combinatorial optimization problems is proposed. This approach makes use of a heuristic algorithm to explore the search space tree of a problem instance. The algorithm is based on Monte Carlo tree search, a popular algorithm in game playing that is used to explore game trees. By leveraging the combinatorial structure of a problem, several enhancements to the algorithm are proposed. These enhancements aim to efficiently explore the search space tree by pruning subtrees, using a heuristic simulation policy, reducing the domain of variables by eliminating dominated solutions and using a beam width. They are demonstrated for a specific combinatorial optimization problem: the quay crane scheduling problem with non-crossing constraints. Computational results show that the proposed algorithm is competitive with the state-of-the-art for this problem and eight new best solutions for a benchmark set of instances are found. Apart from this, the results also show evidence that the algorithm is able to learn to correct the incorrect choices of a standard heuristic, yielding an average improvement of 10.0 % with respect to the objective function value of the solution.

We present a novel framework for design space search on analog circuit sizing using deep reinforcement learning (DRL). Nowadays, analog circuit design is a manual routine that requires heavy design efforts due to the absence of automation tools, motivating the urge to develop one. Prior approaches cast this process as an optimization problem. They use global search strategies based on DRL with complex network architectures. Nonetheless, the models are hard to converge and neglected various working conditions of PVT (process, voltage, temperature).In this work, we reduce the problem to a constraint satisfaction problem, where a local strategy is adopted. Thus, a simple feed-forward network with few layers can be used to implement a model-based reinforcement learning agent. To evaluate the value of the our framework in production, we cooperate with R&Ds in an IC design company. On circuits with TSMC advanced 5 and 6nm process, our agents can deliver PPA (performance, power, area) beyond human level. Furthermore, the product will be taped out in the near future.

In the last decade remarkable progress has been made in development of suitable proof techniques for analysing randomised search heuristics. The theoretical investigation of these algorithms on classes of functions is essential to the understanding of the underlying stochastic process. Linear functions have been traditionally studied in this area resulting in tight bounds on the expected optimisation time of simple randomised search algorithms for this class of problems. Recently, the constrained version of this problem has gained attention and some theoretical results have also been obtained on this class of problems. In this paper we study the class of linear functions under uniform constraint and investigate the expected optimisation time of Randomised Local Search (RLS) and a simple evolutionary algorithm called (1+1) EA. We prove a tight bound of $\Theta(n^2)$ for RLS and improve the previously best known upper bound of (1+1) EA from $O(n^2 \log (Bw_{\max}))$ to $O(n^2\log B)$ in expectation and to $O(n^2 \log n)$ with high probability, where $w_{\max}$ and $B$ are the maximum weight of the linear objective function and the bound of the uniform constraint, respectively. Also, we obtain a tight bound of $O(n^2)$ for the (1+1) EA on a special class of instances. We complement our theoretical studies by experimental investigations that consider different values of $B$ and also higher mutation rates that reflect the fact that $2$-bit flips are crucial for dealing with the uniform constraint.

The above data structures all of these operations can be guaranteed to be in O(Logn) time. So can we perform it with O(1) time? this is why the hash table comes in. The simplest method to build Hash function is each key, we can perform sum of each key by add all character and then we can use Modulo for M. M is typically a prime number and it is the size of Hash array. I just suppose in a simple case of password but in real life, we must encode password (this is not the purpose of this article and apply a ton of algorithm for encoding password).

As a classical and ever reviving topic, change point detection is often formulated as a search for the maximum of a gain function describing improved fits when segmenting the data. Searching through all candidate split points on the grid for finding the best one requires $O(T)$ evaluations of the gain function for an interval with $T$ observations. If each evaluation is computationally demanding (e.g. in high-dimensional models), this can become infeasible. Instead, we propose optimistic search strategies with $O(\log T)$ evaluations exploiting specific structure of the gain function. Towards solid understanding of our strategies, we investigate in detail the classical univariate Gaussian change in mean setup. For some of our proposals we prove asymptotic minimax optimality for single and multiple change point scenarios. Our search strategies generalize far beyond the theoretically analyzed univariate setup. We illustrate, as an example, massive computational speedup in change point detection for high-dimensional Gaussian graphical models. More generally, we demonstrate empirically that our optimistic search methods lead to competitive estimation performance while heavily reducing run-time.

In literature, Clustered Shortest-Path Tree Problem (CluSPT) is an NP-hard problem. Previous studies often search for an optimal solution in relatively large space. To enhance the performance of the search process, two approaches are proposed: the first approach seeks for solutions as a set of edges. From the original graph, we generate a new graph whose vertex set's cardinality is much smaller than that of the original one. Consequently, an effective Evolutionary Algorithm (EA) is proposed for solving CluSPT. The second approach looks for vertex-based solutions. The search space of the CluSPT is transformed into 2 nested search spaces (NSS). With every candidate in the high-level optimization, the search engine in the lower level will find a corresponding candidate to combine with it to create the best solution for CluSPT. Accordingly, Nested Local Search EA (N-LSEA) is introduced to search for the optimal solution on the NSS. When solving this model in lower level by N-LSEA, variety of similar tasks are handled. Thus, Multifactorial Evolutionary Algorithm applied in order to enhance the implicit genetic transfer across these optimizations. Proposed algorithms are conducted on a series of datasets and the obtained results demonstrate superior efficiency in comparison to previous scientific works.

Learning and planning with latent space dynamics has been shown to be useful for sample efficiency in model-based reinforcement learning (MBRL) for discrete and continuous control tasks. In particular, recent work, for discrete action spaces, demonstrated the effectiveness of latent-space planning via Monte-Carlo Tree Search (MCTS) for bootstrapping MBRL during learning and at test time. However, the potential gains from latent-space tree search have not yet been demonstrated for environments with continuous action spaces. In this work, we propose and explore an MBRL approach for continuous action spaces based on tree-based planning over learned latent dynamics. We show that it is possible to demonstrate the types of bootstrapping benefits as previously shown for discrete spaces. In particular, the approach achieves improved sample efficiency and performance on a majority of challenging continuous-control benchmarks compared to the state-of-the-art.