# Feedback Solution to Optimal Switching Problems with Switching Cost

arXiv: https://arxiv.org/abs/1411.4695 · HTML: https://mlsanity.com/paper/1411.4695/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Nov 2014.

## Built on by (most cited first, 3 of 3)

- [Generalized Translation and Scale Invariant Online Algorithm for Adversarial Multi-Armed Bandits](https://mlsanity.com/paper/2109.09212/) (2021)
- [Second Order Regret Bounds Against Generalized Expert Sequences under Partial Bandit Feedback](https://mlsanity.com/paper/2204.06660/) (2022)
- [Data Dependent Regret Guarantees Against General Comparators for Full or Bandit Feedback](https://mlsanity.com/paper/2303.06526/) (2023)

## Abstract (arXiv)

The problem of optimal switching between nonlinear autonomous subsystems is investigated in this study where the objective is not only bringing the states to close to the desired point, but also adjusting the switching pattern, in the sense of penalizing switching occurrences and assigning different preferences to utilization of different modes. The mode sequence is unspecified and a switching cost term is used in the cost function for penalizing each switching. It is shown that once a switching cost is incorporated, the optimal cost-to-go function depends on the already active subsystem, i.e., the subsystem which was engaged in the previous time step. Afterwards, an approximate dynamic programming based method is developed which provides an approximation of the optimal solution to the problem in a feedback form and for different initial conditions. Finally, the performance of the method is analyzed through numerical examples.