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.

Mobile payment such as Alipay has been widely used in our daily lives. To further promote the mobile payment activities, it is important to run marketing campaigns under a limited budget by providing incentives such as coupons, commissions to merchants. As a result, incentive optimization is the key to maximizing the commercial objective of the marketing campaign. With the analyses of online experiments, we found that the transaction network can subtly describe the similarity of merchants' responses to different incentives, which is of great use in the incentive optimization problem. In this paper, we present a graph representation learning method atop of transaction networks for merchant incentive optimization in mobile payment marketing. With limited samples collected from online experiments, our end-to-end method first learns merchant representations based on an attributed transaction networks, then effectively models the correlations between the commercial objectives each merchant may achieve and the incentives under varying treatments. Thus we are able to model the sensitivity to incentive for each merchant, and spend the most budgets on those merchants that show strong sensitivities in the marketing campaign. Extensive offline and online experimental results at Alipay demonstrate the effectiveness of our proposed approach.

We analyze the convergence rate of various momentum-based optimization algorithms from a dynamical systems point of view. Our analysis exploits fundamental topological properties, such as the continuous dependence of iterates on their initial conditions, to provide a simple characterization of convergence rates. In many cases, closed-form expressions are obtained that relate algorithm parameters to the convergence rate. The analysis encompasses discrete time and continuous time, as well as time-invariant and time-variant formulations, and is not limited to a convex or Euclidean setting. In addition, the article rigorously establishes why symplectic discretization schemes are important for momentum-based optimization algorithms, and provides a characterization of algorithms that exhibit accelerated convergence.

This paper presents a novel deep learning based data-driven optimization method. A novel generative adversarial network (GAN) based data-driven distributionally robust chance constrained programming framework is proposed. GAN is applied to fully extract distributional information from historical data in a nonparametric and unsupervised way without a priori approximation or assumption. Since GAN utilizes deep neural networks, complicated data distributions and modes can be learned, and it can model uncertainty efficiently and accurately. Distributionally robust chance constrained programming takes into consideration ambiguous probability distributions of uncertain parameters. To tackle the computational challenges, sample average approximation method is adopted, and the required data samples are generated by GAN in an end-to-end way through the differentiable networks. The proposed framework is then applied to supply chain optimization under demand uncertainty. The applicability of the proposed approach is illustrated through a county-level case study of a spatially explicit biofuel supply chain in Illinois.

Community structure in networks is observed in many different domains, and unsupervised community detection has received a lot of attention in the literature. Increasingly the focus of network analysis is shifting towards using network information in some other prediction or inference task rather than just analyzing the network itself. In particular, in neuroimaging applications brain networks are available for multiple subjects and the goal is often to predict a phenotype of interest. Community structure is well known to be a feature of brain networks, typically corresponding to different regions of the brain responsible for different functions. There are standard parcellations of the brain into such regions, usually obtained by applying clustering methods to brain connectomes of healthy subjects. However, when the goal is predicting a phenotype or distinguishing between different conditions, these static communities from an unrelated set of healthy subjects may not be the most useful for prediction. Here we present a method for supervised community detection, aiming to find a partition of the network into communities that is most useful for predicting a particular response. We use a block-structured regularization penalty combined with a prediction loss function, and compute the solution with a combination of a spectral method and an ADMM optimization algorithm. We show that the spectral clustering method recovers the correct communities under a weighted stochastic block model. The method performs well on both simulated and real brain networks, providing support for the idea of task-dependent brain regions.

We study the estimation of risk-sensitive policies in reinforcement learning problems defined by a Markov Decision Process (MDPs) whose state and action spaces are countably finite. Prior efforts are predominately afflicted by computational challenges associated with the fact that risk-sensitive MDPs are time-inconsistent. To ameliorate this issue, we propose a new definition of risk, which we call caution, as a penalty function added to the dual objective of the linear programming (LP) formulation of reinforcement learning. The caution measures the distributional risk of a policy, which is a function of the policy's long-term state occupancy distribution. To solve this problem in an online model-free manner, we propose a stochastic variant of primal-dual method that uses Kullback-Lieber (KL) divergence as its proximal term. We establish that the number of iterations/samples required to attain approximately optimal solutions of this scheme matches tight dependencies on the cardinality of the state and action spaces, but differs in its dependence on the infinity norm of the gradient of the risk measure. Experiments demonstrate the merits of this approach for improving the reliability of reward accumulation without additional computational burdens.

Gaussian processes (GP) are one of the most successful frameworks to model uncertainty. However, GP optimization (e.g., GP-UCB) suffers from major scalability issues. Experimental time grows linearly with the number of evaluations, unless candidates are selected in batches (e.g., using GP-BUCB) and evaluated in parallel. Furthermore, computational cost is often prohibitive since algorithms such as GP-BUCB require a time at least quadratic in the number of dimensions and iterations to select each batch. In this paper, we introduce BBKB (Batch Budgeted Kernel Bandits), the first no-regret GP optimization algorithm that provably runs in near-linear time and selects candidates in batches. This is obtained with a new guarantee for the tracking of the posterior variances that allows BBKB to choose increasingly larger batches, improving over GP-BUCB. Moreover, we show that the same bound can be used to adaptively delay costly updates to the sparse GP approximation used by BBKB, achieving a near-constant per-step amortized cost. These findings are then confirmed in several experiments, where BBKB is much faster than state-of-the-art methods.

Imitation Learning (IL) is a popular paradigm for training agents to achieve complicated goals by leveraging expert behavior, rather than dealing with the hardships of designing a correct reward function. With the environment modeled as a Markov Decision Process (MDP), most of the existing IL algorithms are contingent on the availability of expert demonstrations in the same MDP as the one in which a new imitator policy is to be learned. This is uncharacteristic of many real-life scenarios where discrepancies between the expert and the imitator MDPs are common, especially in the transition dynamics function. Furthermore, obtaining expert actions may be costly or infeasible, making the recent trend towards state-only IL (where expert demonstrations constitute only states or observations) ever so promising. Building on recent adversarial imitation approaches that are motivated by the idea of divergence minimization, we present a new state-only IL algorithm in this paper. It divides the overall optimization objective into two subproblems by introducing an indirection step and solves the subproblems iteratively. We show that our algorithm is particularly effective when there is a transition dynamics mismatch between the expert and imitator MDPs, while the baseline IL methods suffer from performance degradation. To analyze this, we construct several interesting MDPs by modifying the configuration parameters for the MuJoCo locomotion tasks from OpenAI Gym 1 .

The existence of a saddle point in convex-concave games follows from the celebrated minimax theorem (von Neumann, 1928; Sion et al., 1958) and numerical algorithms for finding it has a long history in optimization (Dem'yanov and Malozemov, 1974; Nemirovsky and Yudin, 1983; Zhang et al., 2019; Lin et al., 2020). Recent success in generative adversarial networks (GANs) (Goodfellow et al., 2014; Heusel et al., 2017) and reinforcement learning (Sutton et al., 1998; Du et al., 2017; Dai et al., 2018) has imposed new challenges for non-convex-non-concave (NCNC) settings. An important question is: what is a local optimal point in min-max optimization? Daskalakis and Panageas (2018) used a local version of saddle points to define local optimality and studied the local convergence behavior of gradient descent (GD) (Arrow et al., 1958) and optimistic gradient descent (OGD) (Popov, 1980; Daskalakis et al., 2018). Following this work, Jin et al. (2019) proposed a new definition of local optimality called local min-max points, and studied how GD converges to such points. One of the difficulties in the NCNC settings is the absence of strong duality (e.g. Boyd and Vandenberghe (2004)), which implies an intrinsic order for min-max optimization, known as Stackelberg games (von Stackelberg, 1934) where a leader takes action first and a follower acts upon the leader's strategy. The global solution to Stackelberg games is well-defined, which we call a global min-max point (a.k.a.

Shape-constrained convex regression problem deals with fitting a convex function to the observed data, where additional constraints are imposed, such as component-wise monotonicity and uniform Lipschitz continuity. This paper provides a comprehensive mechanism for computing the least squares estimator of a multivariate shape-constrained convex regression function in $\mathbb{R}^d$. We prove that the least squares estimator is computable via solving a constrained convex quadratic programming (QP) problem with $(n+1)d$ variables and at least $n(n-1)$ linear inequality constraints, where $n$ is the number of data points. For solving the generally very large-scale convex QP, we design two efficient algorithms, one is the symmetric Gauss-Seidel based alternating direction method of multipliers ({\tt sGS-ADMM}), and the other is the proximal augmented Lagrangian method ({\tt pALM}) with the subproblems solved by the semismooth Newton method ({\tt SSN}). Comprehensive numerical experiments, including those in the pricing of basket options and estimation of production functions in economics, demonstrate that both of our proposed algorithms outperform the state-of-the-art algorithm. The {\tt pALM} is more efficient than the {\tt sGS-ADMM} but the latter has the advantage of being simpler to implement.