scholarly journals Gradient-bounded dynamic programming for submodular and concave extensible value functions with probabilistic performance guarantees

Automatica ◽  
2022 ◽  
Vol 135 ◽  
pp. 109897
Author(s):  
Denis Lebedev ◽  
Paul Goulart ◽  
Kostas Margellos
Keyword(s):  
Dynamic Programming ◽  
Value Functions ◽  
Performance Guarantees

scholarly journals Subgradients of value functions in parametric dynamic programming

2009 ◽  
Vol 193 (1) ◽  
pp. 12-22 ◽  
Author(s):  
B.T. Kien ◽  
Y.C. Liou ◽  
N.-C. Wong ◽  
J.-C. Yao
Keyword(s):  
Dynamic Programming ◽  
Value Functions

APPROXIMATE DYNAMIC PROGRAMMING TECHNIQUES FOR SKILL-BASED ROUTING IN CALL CENTERS

2012 ◽  
Vol 26 (4) ◽  
pp. 581-591 ◽  
Author(s):  
D. Roubos ◽  
S. Bhulai
Keyword(s):  
Dynamic Programming ◽  
Call Center ◽  
Approximate Dynamic Programming ◽  
Call Centers ◽  
Problem Instance ◽  
Value Functions ◽  
Skill Sets ◽  
Programming Techniques ◽  
Optimal Dynamic ◽  
Routing Policies

We consider the problem of dynamic multi-skill routing in call centers. Calls from different customer classes are offered to the call center according to a Poisson process. The agents are grouped into pools according to their heterogeneous skill sets that determine the calls that they can handle. Each pool of agents serves calls with independent exponentially distributed service times. Arriving calls that cannot be served directly are placed in a buffer that is dedicated to the customer class. We obtain nearly optimal dynamic routing policies that are scalable with the problem instance and can be computed online. The algorithm is based on approximate dynamic programming techniques. In particular, we perform one-step policy improvement using a polynomial approximation to relative value functions. We compare the performance of this method with decomposition techniques. Numerical experiments demonstrate that our method outperforms leading routing policies and has close to optimal performance.

scholarly journals Symbolic Dynamic Programming for Continuous State MDPs with Linear Program Transitions

2021 ◽  
Author(s):  
Jihwan Jeong ◽  
Parth Jaggi ◽  
Scott Sanner
Keyword(s):  
Dynamic Programming ◽  
Closed Form ◽  
Piecewise Linear ◽  
Linear Program ◽  
Symbolic Dynamic ◽  
State Transitions ◽  
Traffic Signal Control ◽  
Value Functions ◽  
Continuous State ◽  
Solution Methods

Recent advances in symbolic dynamic programming (SDP) have significantly broadened the class of MDPs for which exact closed-form value functions can be derived. However, no existing solution methods can solve complex discrete and continuous state MDPs where a linear program determines state transitions --- transitions that are often required in problems with underlying constrained flow dynamics arising in problems ranging from traffic signal control to telecommunications bandwidth planning. In this paper, we present a novel SDP solution method for MDPs with LP transitions and continuous piecewise linear dynamics by introducing a novel, fully symbolic argmax operator. On three diverse domains, we show the first automated exact closed-form SDP solution to these challenging problems and the significant advantages of our SDP approach over discretized approximations.

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