GP State Space Model Training via Mutual Information Control Selection
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Solution Overview
Problem
The learning of Gaussian process state space models for controlling robotic devices involves high computational effort and time expenditure.
Innovation Solution
A method for training a Gaussian process state space model by actively selecting control parameters based on mutual information, using a variation inference method to reduce computational effort and time, while accounting for uncertainty and weak dependencies in latent states.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a Gaussian process state space model is learned specifically for a dynamic system, then the model accuracy is improved, but the computational effort and time expenditure increase significantly
Solution Approach 1:
The patent applies preliminary action by pre-computing and storing transition probabilities in lookup tables before the actual training process. The transition function p(x_t|c_{t-1}, x_{t-1}) is calculated in advance for all possible state transitions, allowing the training algorithm to quickly retrieve pre-computed values during iterative optimization without performing complex Gaussian process calculations from scratch at each step.
Solution Approach 2:
The patent segments the training process into distinct computational stages: (1) pre-computation of transition probabilities stored in lookup tables, (2) variational inference optimization using segmented parameter updates, and (3) iterative training with cached intermediate results. This segmentation allows each stage to be optimized independently and reduces redundant computations across iterations.
2Measurement precision
If a Gaussian process state space model is learned specifically for a dynamic system, then the model accuracy is improved, but the computational effort increases significantly
Solution Approach 1:
The patent applies preliminary action by pre-computing and storing transition probabilities in lookup tables before the actual training process. The transition function p(x_t|c_{t-1}, x_{t-1}) is calculated in advance for all possible state transitions, allowing the training algorithm to quickly retrieve pre-computed values during iterative optimization without performing complex Gaussian process calculations from scratch at each step.
Solution Approach 2:
The patent uses copying by creating and storing cached representations of transition probabilities and intermediate computational results in lookup tables. Instead of repeatedly computing the same Gaussian process transitions during each iteration of the variational inference algorithm, the system copies pre-computed probability values and reuses them, significantly reducing computational effort while maintaining model accuracy.
3Productivity
If active learning with mutual information maximization is used to select control parameters, then the training efficiency is improved, but the complexity of the training algorithm increases
Solution Approach 1:
The patent introduces an intermediary mutual information criterion that bridges the selection of control parameters and the training objective. Instead of directly optimizing complex GPSSM parameters, the algorithm uses mutual information I(c_t; y_{1:t}) as an intermediary objective that guides control parameter selection. This intermediary measure simplifies the optimization process by providing a tractable proxy that correlates with overall model training effectiveness.
Solution Approach 2:
The patent implements feedback by using the computed mutual information values to iteratively refine control parameter selections during training. The algorithm calculates mutual information for candidate control parameters, selects those maximizing the criterion, executes corresponding system trajectories, and uses the resulting data to update the GPSSM. This closed-loop feedback process continuously improves training efficiency while maintaining manageable algorithmic complexity through the use of pre-computed lookup tables.
Data Source
AI summary
Training a Gaussian process state space model, which describes a correlation between selected control parameters of a plurality of control parameters for controlling a robotic device and output variables of the robotic device assigned in each case. The method includes: for each control parameter: ascertaining a transitional normal distribution and an output variable normal distribution assigned to a respective predicted output state, ascertaining a respective value of a piece of mutual information between the ascertained output variable normal distribution and the ascertained transitional normal distribution; selecting the control parameter having the highest value of the mutual information as the new control parameter; controlling the robotic device using the new control parameter and measuring an output variable of the robotic device assigned to the new control parameter; and training the Gaussian process state space model using the new control parameter and the assigned measured output variable of the robotic device.