Tool-augmented large language models (LLMs) leverage tools, often in the form of APIs, to improve their reasoning capabilities on complex tasks. This enables them to act as intelligent agents interacting with the real world. The recently introduced ToolLLaMA model by Qin et al. [2023] utilizes the depth-first search-based decision tree (DFSDT) mechanism for multi-step reasoning with $16000+$ real-world APIs, effectively enhancing the performance of tool-augmented LLMs compared to traditional chain reasoning mechanisms. However, their approach only employs successful paths from decision trees (also called inference trees) for supervised fine-tuning (SFT), missing out on the potential learning opportunities from failed paths. Inspired by this, we propose an inference trajectory optimization framework based on preference learning to address this limitation.

Tool-augmented large language models (LLMs) leverage tools, often in the form of APIs, to improve their reasoning capabilities on complex tasks. This enables them to act as intelligent agents interacting with the real world. The recently introduced ToolLLaMA model by Qin et al. [2023] utilizes the depth-first search-based decision tree (DFSDT) mechanism for multi-step reasoning with 16000 real-world APIs, effectively enhancing the performance of tool-augmented LLMs compared to traditional chain reasoning mechanisms. However, their approach only employs successful paths from decision trees (also called inference trees) for supervised fine-tuning (SFT), missing out on the potential learning opportunities from failed paths. Inspired by this, we propose an inference trajectory optimization framework based on preference learning to address this limitation.

We introduce inference trees (ITs), a new class of inference methods that build on ideas from Monte Carlo tree search to perform adaptive sampling in a manner that balances exploration with exploitation, ensures consistency, and alleviates pathologies in existing adaptive methods. ITs adaptively sample from hierarchical partitions of the parameter space, while simultaneously learning these partitions in an online manner. This enables ITs to not only identify regions of high posterior mass, but also maintain uncertainty estimates to track regions where significant posterior mass may have been missed. ITs can be based on any inference method that provides a consistent estimate of the marginal likelihood. They are particularly effective when combined with sequential Monte Carlo, where they capture long-range dependencies and yield improvements beyond proposal adaptation alone.

The problem of subgroups is ubiquitous in scientific research (ex. disease heterogeneity, spatial distributions in ecology...), and piecewise regression is one way to deal with this phenomenon. Morse-Smale regression offers a way to partition the regression function based on level sets of a defined function and that function's basins of attraction. This topologically-based piecewise regression algorithm has shown promise in its initial applications, but the current implementation in the literature has been limited to elastic net and generalized linear regression. It is possible that nonparametric methods, such as random forest or conditional inference trees, may provide better prediction and insight through modeling interaction terms and other nonlinear relationships between predictors and a given outcome. This study explores the use of several machine learning algorithms within a Morse-Smale piecewise regression framework, including boosted regression with linear baselearners, homotopy-based LASSO, conditional inference trees, random forest, and a wide neural network framework called extreme learning machines. Simulations on Tweedie regression problems with varying Tweedie parameter and dispersion suggest that many machine learning approaches to Morse-Smale piecewise regression improve the original algorithm's performance, particularly for outcomes with lower dispersion and linear or a mix of linear and nonlinear predictor relationships. On a real actuarial problem, several of these new algorithms perform as good as or better than the original Morse-Smale regression algorithm, and most provide information on the nature of predictor relationships within each partition to provide insight into differences between dataset partitions.