Explainable dynamic programming

2021 ◽  
Vol 31 ◽  
Author(s):  
MARTIN ERWIG ◽  
PRASHANT KUMAR
Keyword(s):  
Dynamic Programming ◽  
Large Class ◽  
Systematic Approach ◽  
Optimization Algorithms ◽  
Smooth Transition ◽  
Program Execution ◽  
Type Classes ◽  
Dynamic Programs ◽  
The Creation

Abstract In this paper, we present a method for explaining the results produced by dynamic programming (DP) algorithms. Our approach is based on retaining a granular representation of values that are aggregated during program execution. The explanations that are created from the granular representations can answer questions of why one result was obtained instead of another and therefore can increase the confidence in the correctness of program results. Our focus on dynamic programming is motivated by the fact that dynamic programming offers a systematic approach to implementing a large class of optimization algorithms which produce decisions based on aggregated value comparisons. It is those decisions that the granular representation can help explain. Moreover, the fact that dynamic programming can be formalized using semirings supports the creation of a Haskell library for dynamic programming that has two important features. First, it allows programmers to specify programs by recurrence relationships from which efficient implementations are derived automatically. Second, the dynamic programs can be formulated generically (as type classes), which supports the smooth transition from programs that only produce result to programs that can run with granular representation and also produce explanations. Finally, we also demonstrate how to anticipate user questions about program results and how to produce corresponding explanations automatically in advance.

Optimal strategies in measurable learning systems on metric spaces

1977 ◽  
Vol 14 (4) ◽  
pp. 795-805 ◽  
Author(s):  
Ernst–Erich Doberkat
Keyword(s):  
Dynamic Programming ◽  
Metric Spaces ◽  
Optimal Strategies ◽  
Learning Systems ◽  
Decision Models ◽  
Programming Approach ◽  
Learning Models ◽  
Dynamic Programming Approach ◽  
One Stage ◽  
Dynamic Programs

A dynamic programming approach for the investigation of learning systems is taken. Making use of one-stage decision models and dynamic programs, respectively, two learning models are formulated and the existence of optimal strategies for learning in the respective models is proven.

Benchmark Study of Five Optimization Algorithms for Weather Routing

2017 ◽  
Author(s):  
Helong Wang ◽  
Wengang Mao ◽  
Leif Eriksson
Keyword(s):  
Dynamic Programming ◽  
Fuel Consumption ◽  
Optimization Algorithm ◽  
Optimization Algorithms ◽  
Measurement Data ◽  
Shipping Industry ◽  
Advantages And Disadvantages ◽  
Benchmark Study ◽  
Routing Optimization ◽  
Weather Routing

Safety and energy efficiency are two of the key issues in the maritime transport community. A sail plan system, which combines the concepts of weather routing and voyage optimization, are recognized by the shipping industry as an efficient measure to ensure a ship’s safety, gain more economic benefit, and reduce negative effects on our environment. In such a system, the key component is to develop a proper optimization algorithm to generate potential ship routes between a ship’s departure and destination. In the weather routing market, four routing optimization algorithms are commonly used. They are the so-called modified Isochrone and Isopone methods, dynamic programming, threedimensional dynamic programming, and Dijkstra’s algorithm, respectively. Each optimization algorithm has its own advantages and disadvantages to estimate a ship routing with shortest sailing time or/and minimum fuel consumption. This paper will present a benchmark study that compare these algorithms for routing optimization aiming at minimum fuel consumption. A merchant ship sailing in the North Atlantic with full-scale performance measurements, are employed as the case study vessels for the comparison. The ship’s speed/power performance is based on the ISO2015 methods combined with the measurement data. It is expected to demonstrate the pros and cons of different algorithms for the ship’s sail planning.

New Problems in Banking

2011 ◽  
pp. 109-129
Author(s):  
Enid Mumford
Keyword(s):  
Organizational Structure ◽  
Case Studies ◽  
Fast Moving ◽  
Systematic Approach ◽  
White Collar ◽  
Management Of Change ◽  
The Past ◽  
The Creation ◽  
Definition Of

In the last three case studies there has been a logical progression through the management of change, considering first the definition of the problem; second, the development of a strategy for handling it; and third, the creation of an appropriate organizational structure. But, in today’s fast-moving world, there are many situations in which it is difficult to carry out this systematic approach. For example what do we do if change involves a technological jump, bringing with it new problems and challenges which have not been experienced before and which are poorly understood? This happened to white-collar work in the next case study. It has also happened many times in the past and is likely to happen many times in the future.

scholarly journals NON-FORMAL EDUCATION INSTITUTIONS IN THE SYSTEM OF CIVIC BUILDINGS IN UKRAINE

2020 ◽  
Vol 12 (1) ◽  
pp. 20-28
Author(s):  
IRYNA L. KRAVCHENKO
Keyword(s):  
Formal Education ◽  
Systematic Approach ◽  
Public Buildings ◽  
Technical Creativity ◽  
The Creation

The article presents individual positions of the author’s research on the integration of non-formal education institutions in the system of civil buildings of Ukraine. The following scientific views on the phenomenon of non-formal education from related industries are analyzed: pedagogy, sociology, psychology, economics and a systematic approach to education as a phenomenon. The prognostic positions of the development of a typological network of non-formal education institutions in connection with the system of public buildings are described. The links are revealed – system objects of a combination of non-formal education institutions with other public buildings. The stages of the study of this problem are briefly described. The proposal on the creation of a universal educational cluster, as a characteristic of non-formal education institutions, is presented, and an example of the formation of the educational block of the center of scientific and technical creativity based on such a cluster is given.

scholarly journals Digit Sums and Infinite Products

2020 ◽  
Author(s):  
Samin Riasat
Keyword(s):  
Closed Form ◽  
Large Class ◽  
Rational Function ◽  
Systematic Approach ◽  
Infinite Product ◽  
Infinite Products

Consider the sequence un defined as follows: un=+1 if the sum of the base b digits of n is even, and un=−1 otherwise, where we take b=2. Recall that the Woods-Robbins infinite product involves a rational function in n and the sequence un. Although several generalizations of the Woods-Robbins product are known in the literature, no other infinite product involving a rational function in n and the sequence un was known in closed form until recently. In this chapter we introduce a systematic approach to these products, which may be generalized to other values of b. We illustrate the approach by evaluating a large class of similar infinite products.

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