Regression with respect to sensing actions and partial states

In this paper, we present a state-based regression function for planning domains where an agent does not have complete information and may have sensing actions. We consider binary domains and employ the 0-approximation [Son & Baral 2001] to define the regression function. In binary domains, the use of 0-approximation means using 3-valued states. Although planning using this approach is incomplete with respect to the full semantics, we adopt it to have a lower complexity. We prove the soundness and completeness of our regression formulation with respect to the definition of progression. More specifically, we show that (i) a plan obtained through regression for a planning problem is indeed a progression solution of that planning problem, and that (ii) for each plan found through progression, using regression one obtains that plan or an equivalent one. We then develop a conditional planner that utilizes our regression function. We prove the soundness and completeness of our planning algorithm and present experimental results with respect to several well known planning problems in the literature.Comment: 38 page

A State-Based Regression Formulation for Domains with Sensing Actions<br> and Incomplete Information

We present a state-based regression function for planning domains where an agent does not have complete information and may have sensing actions. We consider binary domains and employ a three-valued characterization of domains with sensing actions to define the regression function. We prove the soundness and completeness of our regression formulation with respect to the definition of progression. More specifically, we show that (i) a plan obtained through regression for a planning problem is indeed a progression solution of that planning problem, and that (ii) for each plan found through progression, using regression one obtains that plan or an equivalent one.Comment: 34 pages, 7 Figure

Performance Comparison of Knowledge-Based Dose Prediction Techniques Based on Limited Patient Data.

PurposeThe accuracy of dose prediction is essential for knowledge-based planning and automated planning techniques. We compare the dose prediction accuracy of 3 prediction methods including statistical voxel dose learning, spectral regression, and support vector regression based on limited patient training data.MethodsStatistical voxel dose learning, spectral regression, and support vector regression were used to predict the dose of noncoplanar intensity-modulated radiation therapy (4π) and volumetric-modulated arc therapy head and neck, 4π lung, and volumetric-modulated arc therapy prostate plans. Twenty cases of each site were used for k-fold cross-validation, with k = 4. Statistical voxel dose learning bins voxels according to their Euclidean distance to the planning target volume and uses the median to predict the dose of new voxels. Distance to the planning target volume, polynomial combinations of the distance components, planning target volume, and organ at risk volume were used as features for spectral regression and support vector regression. A total of 28 features were included. Principal component analysis was performed on the input features to test the effect of dimension reduction. For the coplanar volumetric-modulated arc therapy plans, separate models were trained for voxels within the same axial slice as planning target volume voxels and voxels outside the primary beam. The effect of training separate models for each organ at risk compared to all voxels collectively was also tested. The mean squared error was calculated to evaluate the voxel dose prediction accuracy.ResultsStatistical voxel dose learning using separate models for each organ at risk had the lowest root mean squared error for all sites and modalities: 3.91 Gy (head and neck 4π), 3.21 Gy (head and neck volumetric-modulated arc therapy), 2.49 Gy (lung 4π), and 2.35 Gy (prostate volumetric-modulated arc therapy). Compared to using the original features, principal component analysis reduced the 4π prediction error for head and neck spectral regression (-43.9%) and support vector regression (-42.8%) and lung support vector regression (-24.4%) predictions. Principal component analysis was more effective in using all/most of the possible principal components. Separate organ at risk models were more accurate than training on all organ at risk voxels in all cases.ConclusionCompared with more sophisticated parametric machine learning methods with dimension reduction, statistical voxel dose learning is more robust to patient variability and provides the most accurate dose prediction method

Regression-based motion planning

This thesis explores two novel approaches to sample-based motion planning that utilize regressions as continuous function approximations to reduce the memory cost of planning. The first approach, Field Search Trees (FST) provides a solution for single-start planning by iteratively building local regressions of the cost-to-arrive function. The second approach, the Regression Complex (RC), constructs a complex of cells with each cell containing a regression of the distance between any two points on its boundary, creating a useful data structure for any start and goal planning query. We provide formal definitions of both approaches and experimental results of running the algorithms on different simulated robot systems. We conclude that regression-based motion planning provides key advantages over traditional sample-based motion planning in certain cases, but more work is required to extend these approaches into higher dimensional configuration spaces

A Control-variable Regression Monte Carlo Technique for Short-term Electricity Generation Planning

In the day-to-day operation of a power system, the system operator repeatedly solves short-term generation planning problems. When formulating these problems the operators have to weigh the risk of costly failures against increased production costs. The resulting problems are often high-dimensional and various approximations have been suggested in the literature. In this article we formulate the short-term planning problem as an optimal switching problem with delayed reaction. Furthermore, we proposed a control variable technique that can be used in Monte Carlo regression to obtain a computationally efficient numerical algorithm.Comment: 50 pages, 6 figure

Transformer-based Planning for Symbolic Regression

Symbolic regression (SR) is a challenging task in machine learning that involves finding a mathematical expression for a function based on its values. Recent advancements in SR have demonstrated the effectiveness of pretrained transformer-based models in generating equations as sequences, leveraging large-scale pretraining on synthetic datasets and offering notable advantages in terms of inference time over GP-based methods. However, these models primarily rely on supervised pretraining goals borrowed from text generation and overlook equation-specific objectives like accuracy and complexity. To address this, we propose TPSR, a Transformer-based Planning strategy for Symbolic Regression that incorporates Monte Carlo Tree Search into the transformer decoding process. Unlike conventional decoding strategies, TPSR enables the integration of non-differentiable feedback, such as fitting accuracy and complexity, as external sources of knowledge into the transformer-based equation generation process. Extensive experiments on various datasets show that our approach outperforms state-of-the-art methods, enhancing the model's fitting-complexity trade-off, extrapolation abilities, and robustness to noiseComment: Parshin Shojaee and Kazem Meidani contributed equally to this wor

Planning for Sustainability in Small Municipalities: The Influence of Interest Groups, Growth Patterns, and Institutional Characteristics

How and why small municipalities promote sustainability through planning efforts is poorly understood. We analyzed ordinances in 451 Maine municipalities and tested theories of policy adoption using regression analysis.We found that smaller communities do adopt programs that contribute to sustainability relevant to their scale and context. In line with the political market theory, we found that municipalities with strong environmental interests, higher growth, and more formal governments were more likely to adopt these policies. Consideration of context and capacity in planning for sustainability will help planners better identify and benefit from collaboration, training, and outreach opportunities

National Culture\u27s Impact on Effectiveness of Supply Chain Disruption Management

The purpose of this research is to understand the national cultural antecedents that may help explain differences in supply chain disruptions mitigation abilities of companies from different countries. An analysis of survey data on disruption planning and response collected from various organizations worldwide was performed using weighted least square regression and factor analysis. We find that culture influences disruption planning and response. Statistical findings suggest that differences in disruption planning and response abilities between companies from different countries could be partly attributed to national culture. All five Hofstede’s dimensions of national culture, i.e., Power Distance, Individualism, Masculinity, Uncertainty Avoidance, and Long-term Orientation were shown to have a significant positive effect on disruption planning and response. National cultural dimensions and economic status of a country could be effectively used to predict disruption planning and response abilities of companies in various countries. Managers could benefit from our research as it could help them assess disruptions mitigation abilities of their partners located in other countries. Increasing international trade and globalization of supply chains accentuate the importance of our research