Evaluating influence diagrams with decision circuits

Although a number of related algorithms have been developed to evaluate influence diagrams, exploiting the conditional independence in the diagram, the exact solution has remained intractable for many important problems. In this paper we introduce decision circuits as a means to exploit the local structure usually found in decision problems and to improve the performance of influence diagram analysis. This work builds on the probabilistic inference algorithms using arithmetic circuits to represent Bayesian belief networks [Darwiche, 2003]. Once compiled, these arithmetic circuits efficiently evaluate probabilistic queries on the belief network, and methods have been developed to exploit both the global and local structure of the network. We show that decision circuits can be constructed in a similar fashion and promise similar benefits.Comment: Appears in Proceedings of the Twenty-Third Conference on Uncertainty in Artificial Intelligence (UAI2007

Three new sensitivity analysis methods for influence diagrams

Performing sensitivity analysis for influence diagrams using the decision circuit framework is particularly convenient, since the partial derivatives with respect to every parameter are readily available [Bhattacharjya and Shachter, 2007; 2008]. In this paper we present three non-linear sensitivity analysis methods that utilize this partial derivative information and therefore do not require re-evaluating the decision situation multiple times. Specifically, we show how to efficiently compare strategies in decision situations, perform sensitivity to risk aversion and compute the value of perfect hedging [Seyller, 2008].Comment: Appears in Proceedings of the Twenty-Sixth Conference on Uncertainty in Artificial Intelligence (UAI2010

Dynamic programming in in uence diagrams with decision circuits

Decision circuits perform efficient evaluation of influence diagrams, building on the ad- vances in arithmetic circuits for belief net- work inference [Darwiche, 2003; Bhattachar- jya and Shachter, 2007]. We show how even more compact decision circuits can be con- structed for dynamic programming in influ- ence diagrams with separable value functions and conditionally independent subproblems. Once a decision circuit has been constructed based on the diagram's "global" graphical structure, it can be compiled to exploit "lo- cal" structure for efficient evaluation and sen- sitivity analysis.Comment: Appears in Proceedings of the Twenty-Sixth Conference on Uncertainty in Artificial Intelligence (UAI2010

Recurrent Sum-Product-Max Networks for Decision Making in Perfectly-Observed Environments

Recent investigations into sum-product-max networks (SPMN) that generalize sum-product networks (SPN) offer a data-driven alternative for decision making, which has predominantly relied on handcrafted models. SPMNs computationally represent a probabilistic decision-making problem whose solution scales linearly in the size of the network. However, SPMNs are not well suited for sequential decision making over multiple time steps. In this paper, we present recurrent SPMNs (RSPMN) that learn from and model decision-making data over time. RSPMNs utilize a template network that is unfolded as needed depending on the length of the data sequence. This is significant as RSPMNs not only inherit the benefits of SPMNs in being data driven and mostly tractable, they are also well suited for sequential problems. We establish conditions on the template network, which guarantee that the resulting SPMN is valid, and present a structure learning algorithm to learn a sound template network. We demonstrate that the RSPMNs learned on a testbed of sequential decision-making data sets generate MEUs and policies that are close to the optimal on perfectly-observed domains. They easily improve on a recent batch-constrained reinforcement learning method, which is important because RSPMNs offer a new model-based approach to offline reinforcement learning

BHATTACHARJYA & SHACHTER 9 Evaluating influence diagrams with decision circuits

Although a number of related algorithms have been developed to evaluate influence diagrams, exploiting the conditional independence in the diagram, the exact solution has remained intractable for many important problems. In this paper we introduce decision circuits as a means to exploit the local structure usually found in decision problems and to improve the performance of influence diagram analysis. This work builds on the probabilistic inference algorithms using arithmetic circuits to represent Bayesian belief networks [Darwiche, 2003]. Once compiled, these arithmetic circuits efficiently evaluate probabilistic queries on the belief network, and methods have been developed to exploit both the global and local structure of the network. We show that decision circuits can be constructed in a similar fashion and promise similar benefits.