skip to main content


Title: State-Based Recurrent SPMNs for Decision-Theoretic Planning under Partial Observability

The sum-product network (SPN) has been extended to model sequence data with the recurrent SPN (RSPN), and to decision-making problems with sum-product-max networks (SPMN). In this paper, we build on the concepts introduced by these extensions and present state-based recurrent SPMNs (S-RSPMNs) as a generalization of SPMNs to sequential decision-making problems where the state may not be perfectly observed. As with recurrent SPNs, S-RSPMNs utilize a repeatable template network to model sequences of arbitrary lengths. We present an algorithm for learning compact template structures by identifying unique belief states and the transitions between them through a state matching process that utilizes augmented data. In our knowledge, this is the first data-driven approach that learns graphical models for planning under partial observability, which can be solved efficiently. S-RSPMNs retain the linear solution complexity of SPMNs, and we demonstrate significant improvements in compactness of representation and the run time of structure learning and inference in sequential domains.

 
more » « less
Award ID(s):
1815598
NSF-PAR ID:
10339357
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence. Main Track.
Page Range / eLocation ID:
2526 to 2533
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. null (Ed.)
    Sum-product networks (SPN) are knowledge compilation models and are related to other graphical models for efficient probabilistic inference such as arithmetic circuits and AND/OR graphs. Recent investigations into generalizing SPNs have yielded sum-product-max networks (SPMN) which offer a data-driven alternative for decision making that has predominantly relied on handcrafted models. However, SPMNs are not suited for decision-theoretic planning which involves 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 SPNs in being data driven and mostly tractable, they are also well suited for planning problems. We establish soundness conditions on the template network, which guarantee that the resulting SPMN is valid, and present a structure learning algorithm to learn a sound template. RSPMNs learned on a testbed of data sets, some generated using RDDLSim, yield MEUs and policies that are close to the optimal on perfectly-observed domains and easily improve on a recent batch-constrained RL method, which is important because RSPMNs offer a new model-based approach to offline RL. 
    more » « less
  2. Probabilistic Sentential Decision Diagrams (PSDDs) provide efficient methods for modeling and reasoning with probability distributions in the presence of massive logical constraints. PSDDs can also be synthesized from graphical models such as Bayesian networks (BNs) therefore offering a new set of tools for performing inference on these models (in time linear in the PSDD size). Despite these favorable characteristics of PSDDs, we have found multiple challenges in PSDD’s FPGA acceleration. Problems include limited parallelism, data dependency, and small pipeline iterations. In this article, we propose several optimization techniques to solve these issues with novel pipeline scheduling and parallelization schemes. We designed the PSDD kernel with a high-level synthesis (HLS) tool for ease of implementation and verified it on the Xilinx Alveo U250 board. Experimental results show that our methods improve the baseline FPGA HLS implementation performance by 2,200X and the multicore CPU implementation by 20X. The proposed design also outperforms state-of-the-art BN and Sum Product Network (SPN) accelerators that store the graph information in memory. 
    more » « less
  3. null (Ed.)
    Using unreliable information sources generating conflicting evidence may lead to a large uncertainty, which significantly hurts the decision making process. Recently, many approaches have been taken to integrate conflicting data from multiple sources and/or fusing conflicting opinions from different entities. To explicitly deal with uncertainty, a belief model called Subjective Logic (SL), as a variant of Dumpster-Shafer Theory, has been proposed to represent subjective opinions and to merge multiple opinions by offering a rich volume of fusing operators, which have been used to solve many opinion inference problems in trust networks. However, the operators of SL are known to be lack of scalability in inferring unknown opinions from large network data as a result of the sequential procedures of merging multiple opinions. In addition, SL does not consider deriving opinions in the presence of conflicting evidence. In this work, we propose a hybrid inference method that combines SL and Probabilistic Soft Logic (PSL), namely, Collective Subjective Plus, CSL + , which is resistible to highly conflicting evidence or a lack of evidence. PSL can reason a belief in a collective manner to deal with large-scale network data, allowing high scalability based on relationships between opinions. However, PSL does not consider an uncertainty dimension in a subjective opinion. To take benefits from both SL and PSL, we proposed a hybrid approach called CSL + for achieving high scalability and high prediction accuracy for unknown opinions with uncertainty derived from a lack of evidence and/or conflicting evidence. Through the extensive experiments on four semi-synthetic and two real-world datasets, we showed that the CSL + outperforms the state-of-the-art belief model (i.e., SL), probabilistic inference models (i.e., PSL, CSL), and deep learning model (i.e., GCN-VAE-opinion) in terms of prediction accuracy, computational complexity, and real running time. 
    more » « less
  4. Abstract

    Reinforcement learning is a general technique that allows an agent to learn an optimal policy and interact with an environment in sequential decision-making problems. The goodness of a policy is measured by its value function starting from some initial state. The focus of this paper was to construct confidence intervals (CIs) for a policy’s value in infinite horizon settings where the number of decision points diverges to infinity. We propose to model the action-value state function (Q-function) associated with a policy based on series/sieve method to derive its confidence interval. When the target policy depends on the observed data as well, we propose a SequentiAl Value Evaluation (SAVE) method to recursively update the estimated policy and its value estimator. As long as either the number of trajectories or the number of decision points diverges to infinity, we show that the proposed CI achieves nominal coverage even in cases where the optimal policy is not unique. Simulation studies are conducted to back up our theoretical findings. We apply the proposed method to a dataset from mobile health studies and find that reinforcement learning algorithms could help improve patient’s health status. A Python implementation of the proposed procedure is available at https://github.com/shengzhang37/SAVE.

     
    more » « less
  5. null (Ed.)
    Regret minimization has proved to be a versatile tool for tree- form sequential decision making and extensive-form games. In large two-player zero-sum imperfect-information games, mod- ern extensions of counterfactual regret minimization (CFR) are currently the practical state of the art for computing a Nash equilibrium. Most regret-minimization algorithms for tree-form sequential decision making, including CFR, require (i) an exact model of the player’s decision nodes, observation nodes, and how they are linked, and (ii) full knowledge, at all times t, about the payoffs—even in parts of the decision space that are not encountered at time t. Recently, there has been growing interest towards relaxing some of those restric- tions and making regret minimization applicable to settings for which reinforcement learning methods have traditionally been used—for example, those in which only black-box access to the environment is available. We give the first, to our knowl- edge, regret-minimization algorithm that guarantees sublinear regret with high probability even when requirement (i)—and thus also (ii)—is dropped. We formalize an online learning setting in which the strategy space is not known to the agent and gets revealed incrementally whenever the agent encoun- ters new decision points. We give an efficient algorithm that achieves O(T 3/4) regret with high probability for that setting, even when the agent faces an adversarial environment. Our experiments show it significantly outperforms the prior algo- rithms for the problem, which do not have such guarantees. It can be used in any application for which regret minimization is useful: approximating Nash equilibrium or quantal response equilibrium, approximating coarse correlated equilibrium in multi-player games, learning a best response, learning safe opponent exploitation, and online play against an unknown opponent/environment. 
    more » « less