Goal scoring, coherent loss and applications to machine learning
- PDF / 636,088 Bytes
- 38 Pages / 439.37 x 666.142 pts Page_size
- 2 Downloads / 177 Views
Series A
Goal scoring, coherent loss and applications to machine learning Wenzhuo Yang1,2
· Melvyn Sim3 · Huan Xu4
Received: 25 October 2016 / Accepted: 5 March 2019 © Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2019
Abstract Motivated by the binary classification problem in machine learning, we study in this paper a class of decision problems where the decision maker has a list of goals, from which he aims to attain the maximal possible number of goals. In binary classification, this essentially means seeking a prediction rule to achieve the lowest probability of misclassification, and computationally it involves minimizing a (difficult) non-convex, 0–1 loss function. To address the intractability, previous methods consider minimizing the cumulative loss—the sum of convex surrogates of the 0–1 loss of each goal. We revisit this paradigm and develop instead an axiomatic framework by proposing a set of salient properties on functions for goal scoring and then propose the coherent loss approach, which is a tractable upper-bound of the loss over the entire set of goals. We show that the proposed approach yields a strictly tighter approximation to the total loss (i.e., the number of missed goals) than any convex cumulative loss approach while preserving the convexity of the underlying optimization problem. Moreover, this approach, applied to for binary classification, also has a robustness interpretation which builds a connection to robust SVMs. Keywords Satisficing · Goal · Robust optimization · Classification · SVM · Coherent loss
B
Wenzhuo Yang [email protected] Melvyn Sim [email protected] Huan Xu [email protected]
1
Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore
2
SAP Leonardo Machine Learning, Singapore, Singapore
3
Department of Decision Sciences, National University of Singapore, Singapore, Singapore
4
H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, USA
123
W. Yang et al.
Mathematics Subject Classification 90C29
1 Introduction Simon, in his seminal works [42,43], argued that rather than formulating and solving complicated optimization problems, in reality decision makers typically choose the actions that ensure certain aspiration levels being achieved. In other words, a natural decision making paradigm for real-world agent is to seek solutions to satisfy predefined goals. A phenomenon termed “satisficing” by Simon himself [43] has been extensively studied since then (e.g., [7,10,11,16,26]). In practice, decision makers often face goals that either compete for limited resource, or are inherently contradicting. Consequently, some tradeoffs among the goals are sought after, since achieving all goals simultaneously would be impossible. In this paper, we focus on the case where the decision maker is interested in maximizing her goals attainment—a problem we call “goal scoring”. There are many practical examples of goal sco
Data Loading...
