Jonathan Frey, Katrin Baumgärtner, Gianluca Frison, Dirk Reinhardt, Jasper Hoffmann, Leonard Fichtner, Sebastien Gros, Moritz Diehl
原文摘要
The efficient computation of parametric solution sensitivities is a key challenge in the integration of learning-enhanced methods with nonlinear model predictive control, as their availability is crucial for many learning algorithms. This paper discusses the computation of solution sensitivities of general nonlinear programs using the implicit function theorem and smoothed optimality conditions treated in interior-point methods (IPM). We introduce sequential barrier quadratic programming (SBQP), which generalizes SQP with an IPM quadratic programming (QP) solver by allowing the barrier parameter to approach a prescribed nonnegative target value, recovering classical SQP when this target is zero. Previous works are limited to convex or unconstrained formulations, or lack an implementation for efficient sensitivity evaluation. The publication is accompanied by an efficient open-source implementation within the `acados` framework, providing both forward and adjoint sensitivities for general optimal control problems, achieving speedups exceeding 3x over the state-of-the-art solvers `mpc.pytorch` and `cvxpygen`.
Seyed Mahdi B. Azad, Jasper Hoffmann, Iman Nematollahi, Hao Zhu, Abhinav Valada, Joschka Boedecker
原文摘要
Forward-backward (FB) representations provide a powerful framework for learning the successor representation (SR) in continuous spaces by enforcing a low-rank factorization. However, a fundamental spectral mismatch often exists between the high-rank transition dynamics of continuous environments and the low-rank bottleneck of the FB architecture, making accurate low-rank representation learning difficult. In this work, we analyze temporal abstraction as a mechanism to mitigate this mismatch. By characterizing the spectral properties of the transition operator, we show that temporal abstraction acts analogously to a low-pass filter that suppresses high-frequency spectral components. This suppression reduces the effective rank of the induced SR while preserving a formal bound on the resulting value function error. Empirically, we show that this alignment is a key factor for stable FB learning, particularly at high discount factors where bootstrapping becomes error-prone. Our results identify temporal abstraction as a principled mechanism for shaping the spectral structure of the underlying MDP and enabling effective long-horizon representations in continuous control.
Multivariate time series forecasting requires capturing temporal dependencies across multiple scales while accounting for both shared and variable-specific dynamics. Compact forecasting models have emerged as an attractive alternative to increasingly large architectures, but preserving strong predictive performance within tight computational and memory budgets remains challenging. We propose a compact one-layer convolutional framework that learns a shared bank of multi-scale temporal filters of each variable. Lightweight variable-specific scalar weights determine the contribution of each temporal component, enabling the model to capture shared temporal structure while adapting to variable-specific dynamics. The learned weights and filter-output energy further provide a natural signal for structured pruning of convolutional filters, reducing computational complexity with minimal degradation in forecasting performance. We additionally introduce an amplitude-adaptive normalization mechanism that preserves variable-dependent temporal amplitudes. Experiments on multiple datasets demonstrate forecasting performance competitive with state-of-the-art methods while requiring substantially fewer parameters and inference FLOPs and achieving low per-sample latency.