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Found 13 papers, 0 papers with code
Can a Transformer Represent a Kalman Filter?
We revisit the problem of Kalman Filtering in linear dynamical systems and show that Transformers can approximate the Kalman Filter in a strong sense.
Best of Both Worlds in Online Control: Competitive Ratio and Policy Regret
We consider the fundamental problem of online control of a linear dynamical system from two different viewpoints: regret minimization and competitive analysis.
Online estimation and control with optimal pathlength regret
A natural goal when designing online learning algorithms for non-stationary environments is to bound the regret of the algorithm in terms of the temporal variation of the input sequence.
Regret-optimal Estimation and Control
We consider estimation and control in linear time-varying dynamical systems from the perspective of regret minimization.
Regret-Optimal LQR Control
Motivated by competitive analysis in online learning, as a criterion for controller design we introduce the dynamic regret, defined as the difference between the LQR cost of a causal controller (that has only access to past disturbances) and the LQR cost of the \emph{unique} clairvoyant one (that has also access to future disturbances) that is known to dominate all other controllers.
Regret-optimal measurement-feedback control
We consider measurement-feedback control in linear dynamical systems from the perspective of regret minimization.
Regret-optimal control in dynamic environments
We consider control in linear time-varying dynamical systems from the perspective of regret minimization.
The Power of Linear Controllers in LQR Control
We also show that cost of the optimal offline linear policy converges to the cost of the optimal online policy as the time horizon grows large, and consequently the optimal offline linear policy incurs linear regret relative to the optimal offline policy, even in the optimistic setting where the noise is drawn i. i. d from a known distribution.
Online Optimization with Predictions and Non-convex Losses
In this work, we give two general sufficient conditions that specify a relationship between the hitting and movement costs which guarantees that a new algorithm, Synchronized Fixed Horizon Control (SFHC), provides a $1+O(1/w)$ competitive ratio, where $w$ is the number of predictions available to the learner.
Beyond Online Balanced Descent: An Optimal Algorithm for Smoothed Online Optimization
We prove a new lower bound on the competitive ratio of any online algorithm in the setting where the costs are $m$-strongly convex and the movement costs are the squared $\ell_2$ norm.
Smoothed Online Optimization for Regression and Control
We consider Online Convex Optimization (OCO) in the setting where the costs are $m$-strongly convex and the online learner pays a switching cost for changing decisions between rounds.
Smoothed Online Convex Optimization in High Dimensions via Online Balanced Descent
We demonstrate the generality of the OBD framework by showing how, with different choices of "balance," OBD can improve upon state-of-the-art performance guarantees for both competitive ratio and regret, in particular, OBD is the first algorithm to achieve a dimension-free competitive ratio, $3 + O(1/\alpha)$, for locally polyhedral costs, where $\alpha$ measures the "steepness" of the costs.
