New insights into cascade feedback linearization of control systems.
problem Obtaining a cascade feedback linearization for invariant control systems.
method Introducing truncated versions of operators from the calculus of variations to prove new theorems.
result Established new geometry and foundational theorems for future work.
Test for linearizing 2-input systems with 2D feedback.
problem Linearizability of two-input systems by feedback.
method Algorithmic test for 2D endogenous feedback.
result Systematic derivation of flat outputs.
Easy conditions found for simplifying complex systems.
problem Linearizing complex two-input systems.
method Endogenous dynamic feedback with a dimension of at most two.
result Necessary and sufficient conditions for linearizability.
Neural ODEs control graph dynamics with low energy feedback.
problem Controlling complex dynamical systems on graphs.
method Neural Ordinary Differential Equation Control (NODEC) framework.
result NODEC learns low-energy control signals for graph dynamical systems.
Geometric framework for dynamic feedback linearization of control systems with symmetry.
problem Dynamic feedback linearization of control systems with symmetry.
method Geometric framework based on Lie symmetry, systematic procedure for all smooth, generic system trajectories.
result Sufficient condition for dynamic feedback linearizability obtained.
Study absolute equivalence for Pfaffian systems, applying to control systems.
problem Absolute equivalence of Pfaffian systems with specific independence conditions.
method Structural results for Pfaffian systems of corank 3, applied to control systems.
result Dynamic feedback linearization of control systems with 2 inputs.
Advocates a local feedback approach for RL in unknown systems.
problem Finding optimal feedback laws in unknown nonlinear dynamical systems.
method Searches over a local feedback representation consisting of an open-loop sequence and an optimal linear feedback law.
result Results in highly efficient training and superior performance compared to global methods.
A new dual test for forward-flatness simplifies computations.
problem Checking forward-flatness in discrete-time systems.
method A unique sequence of integrable codistributions.
result Computational efficiency and comparison with dynamic feedback linearization.
New algorithm controls linear systems with bandit feedback, achieving optimal regret.
problem Controlling linear systems with bandit feedback under adversarial costs.
method Developed a new algorithm for linear control with memory optimization technique.
result Achieved optimal regret growth proportional to square root of time horizon.
Study uses geometric algebra to analyze credit cycles, revealing dangerous feedback loops.
problem Understanding and predicting dangerous feedback loops in credit cycles.
method Represent economic states as multi-vectors in Clifford algebra, focusing on bivector elements for rotational coupling.
result Geometric relationship between unemployment and credit contraction shifts from simple correlation to dangerous rotational dynamics during crises.
FA algorithm provides convergence guarantees for deep linear networks.
problem Training efficiency and convergence of deep neural networks.
method Theoretical analysis of Feedback Alignment (FA) algorithm for deep linear networks.
result Certain initializations lead to implicit anti-regularization, affecting learning effectiveness.
The paper studies symmetry reduction of control systems and its implications for feedback linearization.
problem Understanding symmetry reduction and its effects on feedback linearizability of control systems.
method Generalizing the notion of transversality of Lie group actions, analyzing the geometry of invariant distributions, and extending the S-G-S test.
result Classification of SFL quotients based on geometric properties of the control system and symmetry group.
Paper solves tracking control for ( x , u ) (x,u) ( x , u ) -flat systems using classical states.
problem Tracking control for ( x , u ) (x,u) ( x , u ) -flat systems. method Quasi-static feedback of classical states.
result Achieves linear, decoupled and asymptotically stable tracking error dynamics.
New algorithm controls systems with unknown, changing losses.
problem Control systems with adversarial perturbations and unknown loss function.
method Efficient sublinear regret algorithm for bandit convex optimization with memory.
result Achieves efficient control with sublinear regret in the presence of unknown, changing losses.
We apply the potential force estimation method to artificial time series of market price produced by a deterministic dealer model. We find that dealers' feedback of linear prediction of market price based on the latest mean price changes plays the central role in the market's potential force. When markets are dominated…
Algorithm for online decision making with unknown dynamics and aggregate feedback.
problem Online decision making with unknown dynamics and aggregate bandit feedback.
method Developed an algorithm based on online mirror descent with a self-concordant barrier regularization and an increasing learning rate schedule.
result Achieved O ( K ) O(\sqrt{K}) O ( K ) regret for the online Markov Decision Process with K K K episodes. Efficient algorithm for unknown linear systems with convex costs.
problem Controlling an unknown linear system with stochastic convex costs.
method Optimism in the Face of Uncertainty paradigm.
result Achieves optimal T \sqrt{T} T regret-rate. Study agnostic feature-based dynamic pricing models with linear policies and noisy valuations.
problem Tackles dynamic pricing with unknown noise and no assumptions on data.
method Studies two agnostic models: linear policy and linear noisy valuation, presenting algorithms and regret bounds.
result Demonstrates no-regret learning is possible under weak assumptions, but noisy feedback is not significantly more useful than bandit feedback.
Survey explores geometric aspects of policy optimization in control systems.
problem Understanding the geometric relationships between control design and optimization.
method Geometric perspective on policy optimization, focusing on parameterization and topology.
result Implications of policy geometry on stability and performance of local search algorithms.
Algorithm reduces control regret for unknown systems.
problem Minimizing control regret for unknown linear systems.
method Novel geometric exploration strategy and polynomial-time algorithms.
result First polynomial-time algorithms with optimal regret bounds.
Study online control of unknown time-varying systems with negative and positive results.
problem Online control of time-varying systems with unknown dynamics.
method Algorithmic upper bounds and lower bounds for different policy classes.
result Sublinear adaptive regret bounds for Disturbance Response policies.
The paper tackles exact linearization and control of flat discrete-time systems.
problem Exact linearization and control of flat nonlinear discrete-time systems.
method Investigates conditions for choosing new inputs and feedbacks that may depend on forward-shifts of the new input.
result Easily verifiable conditions for choosing a feasible input and a new input that minimizes forward-shifts of the flat output.
Use simplified layerwise linear models to understand neural dynamics.
problem Complex neural network dynamics are hard to grasp.
method Apply simplified layerwise linear models to explain neural phenomena.
result Simplified models explain neural collapse, emergence, etc.
SCaLE tackles dynamic regret in noisy bandit feedback with switching costs.
problem Unbounded metric movement costs in bandit online convex optimization.
method SCaLE algorithm for high-dimensional dynamic quadratic hitting costs and ℓ 2 \ell_2 ℓ 2 -norm switching costs, with spectral regret analysis. result First algorithm achieving sub-linear dynamic regret without hitting cost knowledge.
We show LLMs can be locally linear, enabling better control of activations.
problem Suboptimal control of LLM activations during generation.
method Model LLM inference as a linear dynamical system, compute feedback controllers using Jacobians, and adapt classical control theory.
result Robust, fine-grained control of LLM activations across models and tasks.
New RL algorithm handles delayed feedback with posterior sampling.
problem Challenges of delayed feedback in reinforcement learning with linear function approximation.
method Posterior sampling with delayed feedback for value-based RL.
result Achieves optimal regret guarantee with improved computational efficiency.
Improved reinforcement learning algorithm with linear approximation for unknown dynamics.
problem Reinforcement learning with adversarial changing cost functions and bandit feedback.
method Combines mirror-descent and least squares policy evaluation in an auxiliary MDP.
result Obtains an O ~ ( K 6 / 7 ) \widetilde O(K^{6/7}) O ( K 6/7 ) regret bound, significantly improving over previous methods. New method tackles online DR-submodular maximization with improved regret guarantees.
problem Online maximization of non-monotone DR-submodular functions over down-closed convex sets.
method 1/e-linearization through exponential reparametrization, surrogate potential, and reduction to online linear optimization.
result Achieves O ( T 1 / 2 ) O(T^{1/2}) O ( T 1/2 ) static regret with single gradient query per round, improving state of the art. Algorithm for online learning in MDPs with linear function approximation and bandit feedback.
problem Online learning in MDPs with changing reward functions and limited feedback.
method Developed MDP-LinExp3 algorithm with theoretical guarantees.
result Proved regret bounds for MDP-LinExp3 algorithm.
Study learns optimal bidding strategy in auctions with dynamic values and aggregated feedback.
problem Optimizing bidding in auctions with time-dependent values and limited feedback.
method Combines plug-in estimators with differential-equation characterization of optimal policy.
result Achieves near optimal regret bounds for learning optimal policy.
Learning weights in a spiking neural network with hidden neurons, using local, stable and online rules, to control non-linear body dynamics is an open problem. Here, we employ a supervised scheme, Feedback-based Online Local Learning Of Weights (FOLLOW), to train a network of heterogeneous spiking neurons with hidden l…
Extended flatness approach for discrete-time systems considers forward and backward shifts.
problem Defining flatness for discrete-time systems with forward-shifts.
method Introducing backward-shifts to extend flatness definition.
result Extended flat systems maintain key properties like reachability and controllability.
Paper introduces a new framework for optimizing non-convex functions.
problem Optimizing non-convex functions, especially DR-submodular and concave functions.
method Developed a general meta-algorithm to convert linear/quadratic optimization to optimization of upper-linearizable/quadratizable functions.
result Unified approach to concave and DR-submodular optimization problems.
Efficient algorithm converges to Nash equilibrium in bilinear problems with bandit feedback.
problem Learning dynamics in bilinear saddle-point problems with bandit feedback.
method Uncoupled learning algorithm combining experimental design and FTRL with a tailored regularizer.
result Last-iterate convergence rate of i l d e O ( T − 1 / 4 ) ilde{O}(T^{-1/4}) i l d e O ( T − 1/4 ) in high probability. New algorithm reduces reinforcement learning regret for linear MDPs with unknown transitions.
problem Adversarial linear mixture MDPs with bandit feedback and unknown transition.
method Proposes a new algorithm with a least square estimator and self-normalized concentration.
result Achieves improved regret bound with high probability.
Optimal pricing strategy for unknown valuation models with noisy feedback.
problem Minimizing regret in dynamic pricing with unknown valuation functions and noisy feedback.
method Proposes a minimax-optimal algorithm using discretization and data partitioning to handle unknown noise distribution and Lipschitz continuity of valuation functions.
result Achieves minimax-optimal regret bound matching the theoretical lower bound up to logarithmic factors.
Feedback improves ESN performance by 30-60% across various tasks.
problem Reducing computational complexity in ESNs for complex sequential data processing.
method State feedback to modify the internal reservoir state of ESNs.
result Feedback significantly improves ESN performance, reducing error by 30-60%.
New algorithm minimizes cumulative loss in dynamic linear bandits without prior knowledge of comparator switches.
problem Minimizing cumulative loss in dynamic linear bandits with unknown number of switches.
method Combining several bandit algorithms to adapt to unknown number of switches without prior knowledge.
result First algorithm achieving optimal regret guarantee of O ( d ( 1 + S T ) T ) \mathcal{O}\big(\sqrt{d(1+S_T) T}\big) O ( d ( 1 + S T ) T ) up to poly-logarithmic terms. Optimal control in changing systems without strong convexity assumptions.
problem Adversarial changes in convex costs for unknown linear systems.
method Non-convex lower confidence bounds and computationally-efficient regret minimization.
result Achieves T \smash{\sqrt{T}} T -regret rate, optimal compared to best stabilizing controller. This work focuses on dynamic regret of online convex optimization that compares the performance of online learning to a clairvoyant who knows the sequence of loss functions in advance and hence selects the minimizer of the loss function at each step. By assuming that the clairvoyant moves slowly (i.e., the minimizers c…
Modeling HFT interactions reveals market instability.
problem Market instability caused by HFT dynamic coupling.
method Developed a recurrence relations framework to model HFT interactions.
result Unexpected latency and feedback can trigger market instability.
Unified framework for analyzing online convex optimization across various settings.
problem Analyzing online convex optimization in different settings and feedback types.
method Unified framework allowing systematic proposal and analysis of meta-algorithms.
result Comparable regret bounds for various feedback types and adversary types.
New algorithm reduces regret in delayed feedback generalised linear bandits.
problem Regret in delayed feedback generalised linear bandits.
method Adaptation of optimistic algorithm to delayed feedback.
result Achieves a regret bound independent of the horizon's delay penalty.
This paper presents a new causal network learning algorithm (FSNN, Feedback System Neural Network) based on the construction and analysis of a non-linear system of Ordinary Differential Equations (ODEs). The constructed system provides insight into the mechanisms responsible for generating the past and potential future…
Active learning method estimates nonlinear systems efficiently.
problem Identifying nonlinear dynamical systems with continuous states and actions.
method Repeating three steps: trajectory planning, tracking, and re-estimation.
result Estimates nonlinear dynamical systems at a parametric rate.
This paper explores a new form of the linear bandit problem in which the algorithm receives the usual stochastic rewards as well as stochastic feedback about which features are relevant to the rewards, the latter feedback being the novel aspect. The focus of this paper is the development of new theory and algorithms fo…
Learning optimal feedback control laws capable of executing optimal trajectories is essential for many robotic applications. Such policies can be learned using reinforcement learning or planned using optimal control. While reinforcement learning is sample inefficient, optimal control only plans an optimal trajectory fr…
Study shows how to control jump-diffusion processes with stable feedback controls in reinforcement learning.
problem Control jump-diffusion processes with unknown coefficients in reinforcement learning.
method Lipschitz continuous optimal feedback controls, stability analysis of forward-backward SDEs, least-squares algorithm.
result Achieves O ( N ln N ) O(\sqrt{N\ln N}) O ( N ln N ) regret for linear-convex learning problems with jumps.