The emergence of specialized optimization hardware such as CMOS annealers and adiabatic quantum computers carries the promise of solving hard combinatorial optimization problems more efficiently in hardware. Recent work has focused on formulating different combinatorial optimization problems as Ising models, the core mathematical abstraction used by a large number of these hardware platforms, and evaluating the performance of these models when solved on specialized hardware. An interesting area of application is data mining, where combinatorial optimization problems underlie many core tasks. In this work, we focus on consensus clustering (clustering aggregation), an important combinatorial problem that has received much attention over the last two decades. We present two Ising models for consensus clustering and evaluate them using the Fujitsu Digital Annealer, a quantum-inspired CMOS annealer. Our empirical evaluation shows that our approach outperforms existing techniques and is a promising direction for future research.

Machine learning algorithms have made remarkable achievements in the field of artificial intelligence. However, most machine learning algorithms are sensitive to the hyper-parameters. Manually optimizing the hyper-parameters is a common method of hyper-parameter tuning. However, it is costly and empirically dependent. Automatic hyper-parameter optimization (autoHPO) is favored due to its effectiveness. However, current autoHPO methods are usually only effective for a certain type of problems, and the time cost is high. In this paper, we propose an efficient automatic parameter optimization approach, which is based on the mapping from data to the corresponding hyper-parameters. To describe such mapping, we propose a sophisticated network structure. To obtain such mapping, we develop effective network constrution algorithms. We also design strategy to optimize the result futher during the application of the mapping. Extensive experimental results demonstrate that the proposed approaches outperform the state-of-the-art apporaches significantly.

Discovering the causal effect of a decision is critical to nearly all forms of decision-making. In particular, it is a key quantity in drug development, in crafting government policy, and when implementing a real-world machine learning system. Given only observational data, confounders often obscure the true causal effect. Luckily, in some cases, it is possible to recover the causal effect by using certain observed variables to adjust for the effects of confounders. However, without access to the true causal model, finding this adjustment requires brute-force search. In this work, we present an algorithm that exploits auxiliary variables, similar to instruments, in order to find an appropriate adjustment by a gradient-based optimization method. We demonstrate that it outperforms practical alternatives in estimating the true causal effect, without knowledge of the full causal graph.

Pay-per-click advertising includes various formats (\emph{e.g.}, search, contextual, social) with a total investment of more than 200 billion USD per year worldwide. An advertiser is given a daily budget to allocate over several, even thousands, campaigns, mainly distinguishing for the ad, target, or channel. Furthermore, publishers choose the ads to display and how to allocate them employing auctioning mechanisms, in which every day the advertisers set for each campaign a bid corresponding to the maximum amount of money per click they are willing to pay and the fraction of the daily budget to invest. In this paper, we study the problem of automating the online joint bid/daily budget optimization of pay-per-click advertising campaigns over multiple channels. We formulate our problem as a combinatorial semi-bandit problem, which requires solving a special case of the Multiple-Choice Knapsack problem every day. Furthermore, for every campaign, we capture the dependency of the number of clicks on the bid and daily budget by Gaussian Processes, thus requiring mild assumptions on the regularity of these functions. We design four algorithms and show that they suffer from a regret that is upper bounded with high probability as O(sqrt{T}), where T is the time horizon of the learning process. We experimentally evaluate our algorithms with synthetic settings generated from real data from Yahoo!, and we present the results of the adoption of our algorithms in a real-world application with a daily average spent of 1,000 Euros for more than one year.

We develop two novel randomized primal-dual algorithms to solve nonsmooth composite convex optimization problems. The first algorithm is fully randomized, i.e., it has randomized updates on both primal and dual variables, while the second one is a semi-randomized scheme which only has one randomized update on the primal (or dual) variable while using the full update for the other. Both algorithms achieve the best-known $\mathcal{O}(1/k)$ or $\mathcal{O}(1/k^2)$ convergence rates in expectation under either only convexity or strong convexity, respectively, where $k$ is the iteration counter. Interestingly, with new parameter update rules, our algorithms can achieve $o(1/k)$ or $o(1/k^2)$ best-iterate convergence rate in expectation under either convexity or strong convexity, respectively. These rates can be obtained for both the primal and dual problems. To the best of our knowledge, this is the first time such faster convergence rates are shown for randomized primal-dual methods. Finally, we verify our theoretical results via two numerical examples and compare them with the state-of-the-art.

The Lipschitz constant of a neural network is a useful metric for provable robustness and generalization. We present a novel analytic result which relates gradient norms to Lipschitz constants for nondifferentiable functions. Next we prove hardness and inapproximability results for computing the local Lipschitz constant of ReLU neural networks. We develop a mixed-integer programming formulation to exactly compute the local Lipschitz constant for scalar and vector-valued networks. Finally, we apply our technique on networks trained on synthetic datasets and MNIST, drawing observations about the tightness of competing Lipschitz estimators and the effects of regularized training on Lipschitz constants.

Bayesian optimization is an efficient nonlinear optimization method where the queries are carefully selected to gather information about the optimum location. Thus, in the context of policy search, it has been called active policy search. The main ingredients of Bayesian optimization for sample efficiency are the probabilistic surrogate model and the optimal decision heuristics. In this work, we exploit those to provide robustness to different issues for policy search algorithms. We combine several methods and show how their interaction works better than the sum of the parts. First, to deal with input noise and provide a safe and repeatable policy we use an improved version of unscented Bayesian optimization. Then, to deal with mismodeling errors and improve exploration we use stochastic meta-policies for query selection and an adaptive kernel. We compare the proposed algorithm with previous results in several optimization benchmarks and robot tasks, such as pushing objects with a robot arm, or path finding with a rover.

We consider online learning for episodic Markov decision processes (MDPs) with stochastic long-term budget constraints, which plays a central role in ensuring the safety of reinforcement learning. Here the loss function can vary arbitrarily across the episodes, whereas both the loss received and the budget consumption are revealed at the end of each episode. Previous works solve this problem under the restrictive assumption that the transition model of the MDP is known a priori and establish regret bounds that depend polynomially on the cardinalities of the state space $\mathcal{S}$ and the action space $\mathcal{A}$. In this work, we propose a new \emph{upper confidence primal-dual} algorithm, which only requires the trajectories sampled from the transition model. In particular, we prove that the proposed algorithm achieves $\tilde{\mathcal{O}}(L|\mathcal{S}|\sqrt{|\mathcal{A}|T})$ upper bounds of both the regret and the constraint violation, where $L$ is the length of each episode. Our analysis incorporates a new high-probability drift analysis of Lagrange multiplier processes into the celebrated regret analysis of upper confidence reinforcement learning, which demonstrates the power of "optimism in the face of uncertainty" in constrained online learning.

Nonlinear constrained optimization problems are an important class of problems with a broad range of engineering, and scientific applications. In this article, we will see how the refashioning of simple unconstrained Optimization techniques leads to a hybrid algorithm for constrained optimization problems. Later, we will observe the robustness of the algorithm through a detailed analysis of a problem set and monitor the performance of optima by comparing the results with some of the inbuilt functions in python. Many engineering design and decision making problems have an objective of optimizing a function and simultaneously have a requirement for satisfying some constraints arising due to space, strength, or stability considerations. So, Constrained optimization refers to the process of optimizing an objective function with respect to some variables in the presence of constraint of those variables.

Differential Evolution (DE) is quite powerful for real parameter single objective optimization. However, the ability of extending or changing search area when falling into a local optimum is still required to be developed in DE for accommodating extremely complicated fitness landscapes with a huge number of local optima. We propose a new flow of DE, termed DE with individuals redistribution, in which a process of individuals redistribution will be called when progress on fitness is low for generations. In such a process, mutation and crossover are standardized, while trial vectors are all kept in selection. Once diversity exceeds a predetermined threshold, our opposition replacement is executed, then algorithm behavior returns to original mode. In our experiments based on two benchmark test suites, we apply individuals redistribution in ten DE algorithms. Versions of the ten DE algorithms based on individuals redistribution are compared with not only original version but also version based on complete restart, where individuals redistribution and complete restart are based on the same entry criterion. Experimental results indicate that, for most of the DE algorithms, version based on individuals redistribution performs better than both original version and version based on complete restart.