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Automatic basis function construction for approximate dynamic programming and reinforcement learning
- Learning. Proceedings of the 23rd International Conference on Machine Learning
, 2006
"... We address the problem of automatically constructing basis functions for linear approximation of the value function of a Markov Decision Process (MDP). Our work builds on results by Bertsekas and Castañon (1989) who proposed a method for automatically aggregating states to speed up value iteration. ..."
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Cited by 39 (0 self)
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We address the problem of automatically constructing basis functions for linear approximation of the value function of a Markov Decision Process (MDP). Our work builds on results by Bertsekas and Castañon (1989) who proposed a method for automatically aggregating states to speed up value iteration. We propose to use neighborhood component analysis (Goldberger et al., 2005), a dimensionality reduction technique created for supervised learning, in order to map a high-dimensional state space to a lowdimensional space, based on the Bellman error, or on the temporal difference (TD) error. We then place basis function in the lower-dimensional space. These are added as new features for the linear function approximator. This approach is applied to a high-dimensional inventory control problem. 1.
Solving Factored MDPs with Hybrid State and Action Variables
- JOURNAL OF ARTIFICIAL INTELLIGENCE RESEARCH
, 2006
"... Efficient representations and solutions for large decision problems with continuous and discrete variables are among the most important challenges faced by the designers of automated decision support systems. In this paper, we describe a novel hybrid factored Markov decision process (MDP) model t ..."
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Cited by 13 (2 self)
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Efficient representations and solutions for large decision problems with continuous and discrete variables are among the most important challenges faced by the designers of automated decision support systems. In this paper, we describe a novel hybrid factored Markov decision process (MDP) model that allows for a compact representation of these problems, and a new hybrid approximate linear programming (HALP) framework that permits their efficient solutions. The central idea of HALP is to approximate the optimal value function by a linear combination of basis functions and optimize its weights by linear programming.
Practical solution techniques for first-order mdps
- Artificial Intelligence
"... Many traditional solution approaches to relationally specified decision-theoretic planning problems (e.g., those stated in the probabilistic planning domain description language, or PPDDL) ground the specification with respect to a specific instantiation of domain objects and apply a solution approa ..."
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Cited by 9 (1 self)
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Many traditional solution approaches to relationally specified decision-theoretic planning problems (e.g., those stated in the probabilistic planning domain description language, or PPDDL) ground the specification with respect to a specific instantiation of domain objects and apply a solution approach directly to the resulting ground Markov decision process (MDP). Unfortunately, the space and time complexity of these grounded solution approaches are polynomial in the number of domain objects and exponential in the predicate arity and the number of nested quantifiers in the relational problem specification. An alternative to grounding a relational planning problem is to tackle the problem directly at the relational level. In this article, we propose one such approach that translates an expressive subset of the PPDDL representation to a first-order MDP (FOMDP) specification and then derives a domain-independent policy without grounding at any intermediate step. However, such generality does not come without its own set of challenges—the purpose of this article is to explore practical solution techniques for solving FOMDPs. To demonstrate the applicability of our techniques, we present proof-of-concept results of our first-order approximate linear programming (FOALP) planner on problems from the probabilistic track
Solving Factored MDPs with Exponential-Family Transition Models
- In Proceedings of the 16th International Conference on Automated Planning and Scheduling
, 2006
"... Markov decision processes (MDPs) with discrete and continuous state and action components can be solved efficiently by hybrid approximate linear programming (HALP). The main idea of the approach is to approximate the optimal value function by a linear combination of basis functions and optimize ..."
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Cited by 6 (4 self)
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Markov decision processes (MDPs) with discrete and continuous state and action components can be solved efficiently by hybrid approximate linear programming (HALP). The main idea of the approach is to approximate the optimal value function by a linear combination of basis functions and optimize it by linear programming. In this paper, we extend the existing HALP paradigm beyond the mixture of beta transition model.
Critical factors in the empirical performance of temporal difference and evolutionary methods for reinforcement learning
- AUTON AGENT MULTI-AGENT SYST
, 2009
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Adaptive Tile Coding for Value Function Approximation
"... Reinforcement learning problems are commonly tackled by estimating the optimal value function. In many real-world problems, learning this value function requires a function approximator, which maps states to values via a parameterized function. In practice, the success of function approximators depe ..."
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Cited by 2 (0 self)
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Reinforcement learning problems are commonly tackled by estimating the optimal value function. In many real-world problems, learning this value function requires a function approximator, which maps states to values via a parameterized function. In practice, the success of function approximators depends on the ability of the human designer to select an appropriate representation for the value function. This paper presents adaptive tile coding, a novel method that automates this design process for tile coding, a popular function approximator, by beginning with a simple representation with few tiles and refining it during learning by splitting existing tiles into smaller ones. In addition to automatically discovering effective representations, this approach provides a natural way to reduce the function approximator’s level of generalization over time. Empirical results in multiple domains compare two different criteria for deciding which tiles to split and verify that adaptive tile coding can automatically discover effective representations and that its speed of learning is competitive with the best fixed representations.
Learning Basis Functions in Hybrid Domains
- In Proceedings of the 21st National Conference on Artificial Intelligence
, 2006
"... Markov decision processes (MDPs) with discrete and continuous state and action components can be solved efficiently by hybrid approximate linear programming (HALP). The main idea of the approach is to approximate the optimal value function by a set of basis functions and optimize their weights b ..."
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Markov decision processes (MDPs) with discrete and continuous state and action components can be solved efficiently by hybrid approximate linear programming (HALP). The main idea of the approach is to approximate the optimal value function by a set of basis functions and optimize their weights by linear programming. The quality of this approximation naturally depends on its basis functions. However, basis functions leading to good approximations are rarely known in advance.
A New Approach for Value Function Approximation Based on Automatic State Partition
"... Abstract—Value function is usually used to deal with the reinforcement learning problems. In large or even continuous states, function approximation must be used to represent value function. Much of the current work carried out, however, has to design the structure of function approximation in advan ..."
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Abstract—Value function is usually used to deal with the reinforcement learning problems. In large or even continuous states, function approximation must be used to represent value function. Much of the current work carried out, however, has to design the structure of function approximation in advanced which cannot be adjusted during learning. In this paper, we propose a novel function approximation called Fuzzy CMAC (FCMAC) with automatic state partition (ASP-FCMAC) to automate the structure design for FCMAC. Based on CMAC (also known as tile coding), ASP-FCMAC employs fuzzy membership function to avoid the setting of parameter in CMAC, and makes use of Bellman error to partition the state automatically so as to generate the structure of FC-MAC. Empirical results in both mountain car and RoboCup Keepaway domains demonstrate that ASP-FCMAC can automatically generate the structure of FCMAC and agent using it can learn efficiently.
Using Mathematical Programming to Solve Factored Markov Decision Processes with Imprecise Probabilities
"... This paper investigates Factored Markov Decision Processes with Imprecise Probabilities (MDPIPs); that is, Factored Markov Decision Processes (MDPs) where transition probabilities are imprecisely specified. We derive efficient approximate solutions for Factored MDPIPs based on mathematical programmi ..."
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This paper investigates Factored Markov Decision Processes with Imprecise Probabilities (MDPIPs); that is, Factored Markov Decision Processes (MDPs) where transition probabilities are imprecisely specified. We derive efficient approximate solutions for Factored MDPIPs based on mathematical programming. To do this, we extend previous linear programming approaches for linear approximations in Factored MDPs, resulting in a multilinear formulation for robust “maximin ” linear approximations in Factored MDPIPs. By exploiting the factored structure in MDPIPs we are able to demonstrate orders of magnitude reduction in solution time over standard exact non-factored approaches, in exchange for relatively low approximation errors, on a difficult class of benchmark problems with millions of states.

