We look at whether machine learning can predict the final objective function value of a difficult combinatorial optimisation problem from the input. Our context is the pattern reduction problem, one industrially important but difficult aspect of the cutting stock problem. Machine learning appears to have higher prediction accuracy than a na\"ive model, reducing mean absolute percentage error (MAPE) from 12.0% to 8.7%.

The identification of synthetic routes that end with a desired product has been an inherently time-consuming process that is largely dependent on expert knowledge regarding a limited fraction of the entire reaction space. At present, emerging machine-learning technologies are overturning the process of retrosynthetic planning. The objective of this study is to discover synthetic routes backwardly from a given desired molecule to commercially available compounds. The problem is reduced to a combinatorial optimization task with the solution space subject to the combinatorial complexity of all possible pairs of purchasable reactants. We address this issue within the framework of Bayesian inference and computation. The workflow consists of two steps: a deep neural network is trained that forwardly predicts a product of the given reactants with a high level of accuracy, following which this forward model is inverted into the backward one via Bayes' law of conditional probability. Using the backward model, a diverse set of highly probable reaction sequences ending with a given synthetic target is exhaustively explored using a Monte Carlo search algorithm. The Bayesian retrosynthesis algorithm could successfully rediscover 80.3% and 50.0% of known synthetic routes of single-step and two-step reactions within top-10 accuracy, respectively, thereby outperforming state-of-the-art algorithms in terms of the overall accuracy. Remarkably, the Monte Carlo method, which was specifically designed for the presence of diverse multiple routes, often revealed a ranked list of hundreds of reaction routes to the same synthetic target. We investigated the potential applicability of such diverse candidates based on expert knowledge from synthetic organic chemistry.

We consider the problem of searching for an unknown target vertex $t$ in a (possibly edge-weighted) graph. Each \emph{vertex-query} points to a vertex $v$ and the response either admits $v$ is the target or provides any neighbor $s\not=v$ that lies on a shortest path from $v$ to $t$. This model has been introduced for trees by Onak and Parys [FOCS 2006] and for general graphs by Emamjomeh-Zadeh et al. [STOC 2016]. In the latter, the authors provide algorithms for the error-less case and for the independent noise model (where each query independently receives an erroneous answer with known probability $p<1/2$ and a correct one with probability $1-p$). We study this problem in both adversarial errors and independent noise models. First, we show an algorithm that needs $\frac{\log_2 n}{1 - H(r)}$ queries against \emph{adversarial} errors, where adversary is bounded with its rate of errors by a known constant $r<1/2$. Our algorithm is in fact a simplification of previous work, and our refinement lies in invoking amortization argument. We then show that our algorithm coupled with Chernoff bound argument leads to an algorithm for independent noise that is simpler and with a query complexity that is both simpler and asymptotically better to one of Emamjomeh-Zadeh et al. [STOC 2016]. Our approach has a wide range of applications. First, it improves and simplifies Robust Interactive Learning framework proposed by Emamjomeh-Zadeh et al. [NIPS 2017]. Secondly, performing analogous analysis for \emph{edge-queries} (where query to edge $e$ returns its endpoint that is closer to target) we actually recover (as a special case) noisy binary search algorithm that is asymptotically optimal, matching the complexity of Feige et al. [SIAM J. Comput. 1994]. Thirdly, we improve and simplify upon existing algorithm for searching of \emph{unbounded} domains due to Aslam and Dhagat [STOC 1991].

We propose the Generalized Policy Elimination (GPE) algorithm, an oracle-efficient contextual bandit (CB) algorithm inspired by the Policy Elimination algorithm of \cite{dudik2011}. We prove the first regret optimality guarantee theorem for an oracle-efficient CB algorithm competing against a nonparametric class with infinite VC-dimension. Specifically, we show that GPE is regret-optimal (up to logarithmic factors) for policy classes with integrable entropy. For classes with larger entropy, we show that the core techniques used to analyze GPE can be used to design an $\varepsilon$-greedy algorithm with regret bound matching that of the best algorithms to date. We illustrate the applicability of our algorithms and theorems with examples of large nonparametric policy classes, for which the relevant optimization oracles can be efficiently implemented.

We consider the problem faced by a recommender system which seeks to offer a user with unknown preferences an item. Before making a recommendation, the system has the opportunity to elicit the user's preferences by making queries. Each query corresponds to a pairwise comparison between items. We take the point of view of either a risk averse or regret averse recommender system which only possess set-based information on the user utility function. We investigate: a) an offline elicitation setting, where all queries are made at once, and b) an online elicitation setting, where queries are selected sequentially over time. We propose exact robust optimization formulations of these problems which integrate the elicitation and recommendation phases and study the complexity of these problems. For the offline case, where the problem takes the form of a two-stage robust optimization problem with decision-dependent information discovery, we provide an enumeration-based algorithm and also an equivalent reformulation in the form of a mixed-binary linear program which we solve via column-and-constraint generation. For the online setting, where the problem takes the form of a multi-stage robust optimization problem with decision-dependent information discovery, we propose a conservative solution approach. We evaluate the performance of our methods on both synthetic data and real data from the Homeless Management Information System. We simulate elicitation of the preferences of policy-makers in terms of characteristics of housing allocation policies to better match individuals experiencing homelessness to scarce housing resources. Our framework is shown to outperform the state-of-the-art techniques from the literature.

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.

Thompson sampling is one of the most widely used algorithms for many online decision problems, due to its simplicity in implementation and superior empirical performance over other state-of-the-art methods. Despite its popularity and empirical success, it has remained an open problem whether Thompson sampling can achieve the minimax optimal regret $O(\sqrt{KT})$ for $K$-armed bandit problems, where $T$ is the total time horizon. In this paper, we solve this long open problem by proposing a new Thompson sampling algorithm called MOTS that adaptively truncates the sampling result of the chosen arm at each time step. We prove that this simple variant of Thompson sampling achieves the minimax optimal regret bound $O(\sqrt{KT})$ for finite time horizon $T$ and also the asymptotic optimal regret bound when $T$ grows to infinity as well. This is the first time that the minimax optimality of multi-armed bandit problems has been attained by Thompson sampling type of algorithms.

Almost all neural architecture search methods are evaluated in terms of performance (i.e. test accuracy) of the model structures that it finds. Should it be the only metric for a good autoML approach? To examine aspects beyond performance, we propose a set of criteria aimed at evaluating the core of autoML problem: the amount of human intervention required to deploy these methods into real world scenarios. Based on our proposed evaluation checklist, we study the effectiveness of a random search strategy for fully automated multimodal neural architecture search. Compared to traditional methods that rely on manually crafted feature extractors, our method selects each modality from a large search space with minimal human supervision. We show that our proposed random search strategy performs close to the state of the art on the AV-MNIST dataset while meeting the desirable characteristics for a fully automated design process.

With modern requirements, there is an increasing tendancy of considering multiple objectives/criteria simultaneously in many Software Engineering (SE) scenarios. Such a multi-objective optimization scenario comes with an important issue --- how to evaluate the outcome of optimization algorithms, which typically is a set of incomparable solutions (i.e., being Pareto non-dominated to each other). This issue can be challenging for the SE community, particularly for practitioners of Search-Based SE (SBSE). On one hand, multiobjective optimization may still be relatively new to SE/SBSE researchers, who may not be able to identify right evaluation methods for their problems. On the other hand, simply following the evaluation methods for general multiobjective optimisation problems may not be appropriate for specific SE problems, especially when the problem nature or decision maker's preferences are explicitly/implicitly available. This has been well echoed in the literature by various inappropriate/inadequate selection and inaccurate/misleading uses of evaluation methods. In this paper, we carry out a critical review of quality evaluation for multiobjective optimization in SBSE. We survey 717 papers published between 2009 and 2019 from 36 venues in 7 repositories, and select 97 prominent studies, through which we identify five important but overlooked issues in the area. We then conduct an in-depth analysis of quality evaluation indicators and general situations in SBSE, which, together with the identified issues, enables us to provide a methodological guidance to selecting and using evaluation methods in different SBSE scenarios.

Program verification techniques typically focus on finding counterexamples that violate properties of a program. Constraint programming offers a convenient way to verify programs by modeling their state transformations and specifying searches that seek counterexamples. Floating-point computations present additional challenges for verification given the semantic subtleties of floating point arithmetic. This paper focuses on search strategies for CSPs using floating point numbers constraint systems and dedicated to program verification. It introduces a new search heuristic based on the global number of occurrences that outperforms state-of-the-art strategies. More importantly, it demonstrates that a new technique that only branches on input variables of the verified program improve performance. It composes with a diversification technique that prevents the selection of the same variable within a fixed horizon further improving performances and reduces disparities between various variable choice heuristics. The result is a robust methodology that can tailor the search strategy according to the sought properties of the counter example.