Exact solution for sparse-reward MDPs with minimal state space dependence.
problem Finding optimal policies for MDPs with sparse rewards and large state spaces.
method Proposes an algorithm with time complexity O ( ∣ R ∣ 3 i m e s ∣ A ∣ 2 ) O( |R|^3 imes |A|^2 ) O ( ∣ R ∣ 3 im es ∣ A ∣ 2 ) and memory complexity O ( ∣ R ∣ i m e s ∣ A ∣ ) O( |R| imes |A| ) O ( ∣ R ∣ im es ∣ A ∣ ) for exact computation. result Exact policy computation without state space dependency for sparse-reward MDPs.
Improved DNN robustness to adversarial attacks using data-dependent activation and total variation minimization.
problem Improving Deep Neural Network robustness to adversarial attacks.
method Data-dependent activation function and total variation minimization.
result Robust accuracy of adversarially trained ResNet20 increased from ~46% to ~69% under IFGSM attack.
The paper tackles estimation of hidden state LTI systems of unknown order.
problem Estimation of Markov parameters and minimal realization of unknown order LTI systems.
method Hankel penalized least square estimator, Ho-Kalman algorithm, and a combined algorithm.
result Statistical guarantees for estimation error, rank recovery, and sample complexity.
We develop a new method to estimate failure probabilities in complex systems.
problem Estimating failure probabilities in safety-critical autonomous systems is challenging due to the rarity of failures and large state spaces.
method We propose an adaptive importance sampling algorithm that minimizes forward Kullback-Leibler divergence and uses Markov score ascent methods.
result Our method provides more accurate failure probability estimates than existing techniques.
State-space systems generate probabilistic dependencies between inputs and outputs.
problem Understanding probabilistic dependencies in state-space systems.
method Introducing a probabilistic framework and proving sufficient conditions for output existence and uniqueness.
result State-space systems can generate probabilistic dependencies, even without functional relations.
Study proves no minimal surfaces can be contained in certain half-spaces or cones.
problem Prohibiting minimal surfaces from certain geometric configurations.
method Analyzes weighted minimal surfaces in R 3 \mathbb{R}^3 R 3 with height-dependent weights. result No proper surfaces can be contained in specific half-spaces or cones.
Paper models non-linear dynamics from time series data.
problem Modeling non-linear dynamical systems from time series data.
method Introduces latent state modeling and a novel alternating minimization algorithm.
result LaNoLem achieves competitive performance in dynamics estimation and prediction.
New algorithm learns optimal policies efficiently with minimal memory.
problem Optimal policy learning in large-scale MDPs.
method Bilinear π learning using state and action features.
result Sample-efficient, solving optimal policy with linear sample complexity.
Algorithm reduces exploration in structured RL problems.
problem Minimize exploration in reinforcement learning with known structure.
method Directed Exploration Learning (DEL) for Lipschitz MDPs.
result Regret lower bounds not scaling with state and action space sizes.
Study complex properties of minimal Lagrangian submanifolds in Kaehler spaces.
problem Complex properties of minimal Lagrangian submanifolds in Kaehler spaces.
method Mix of holomorphic curve techniques and convexity results.
result Minimal Lagrangians do not admit fillings by holomorphic discs in negative curvature case.
Study on high-codimensional minimal surfaces in hyperbolic space.
problem Understanding high-codimensional minimal surfaces in hyperbolic space.
method Investigating asymptotic behavior and boundary regularity of area-minimizing currents.
result Established boundary regularity results for high-codimensional minimal surfaces near their asymptotic boundaries.
Develops a new exponential map for time-varying vector fields.
problem Lack of global flows for general time-varying vector fields.
method Categorical development of spaces of vector fields and flows, allowing for systematic localisation.
result Derives the homeomorphism of the exponential map for vector fields with measurable time-dependence.
Study efficient algorithms for nonconvex optimization with state-dependent Markov data.
problem Stochastic optimization with Markovian data and state-dependent transition kernels.
method Projection-based and projection-free algorithms for constrained nonconvex problems.
result The number of oracle calls to achieve an ε ε ε -stationary point is O ( 1 / ε 2.5 ) \mathcal{O}(1/ε^{2.5}) O ( 1/ ε 2.5 ) . Connected space of Dirac-minimal metrics in 2 and 4 dimensions.
problem Finding metrics with optimal index bounds.
method Using index theory and Dirac operator properties.
result Space of Dirac-minimal metrics is connected in dimensions 2 and 4.
Defines a measure of knot concordance using cobordism distance.
problem Measuring how close knots are to being linearly dependent.
method Cobordism distance on cyclic subgroups of knot concordance group.
result Projective space of knot concordance group with integer-valued metric.
Noise-ignorant empirical risk minimization achieves state-of-the-art performance on noisy data.
problem Learning with noisy labels in multi-class classification problems.
method Introducing relative signal strength (RSS) to quantify transferability and applying Noise Ignorant Empirical Risk Minimization (NI-ERM).
result NI-ERM achieves state-of-the-art performance on CIFAR-N data challenge.
Study finds minimal hypersurfaces in compact symmetric spaces have a linear index bound.
problem Understanding minimal hypersurfaces in compact symmetric spaces.
method Introduced a generalized isometric immersion structure for compact symmetric spaces, proving bounds on the index and nullity.
result Minimal hypersurfaces in compact symmetric spaces have a linear index bound, depending on the first Betti number.
Optimal search for change point anomaly in multiple processes.
problem Detecting a change point in an anomalous process among multiple normal processes.
method Deterministic search algorithm balancing sample complexity and detection accuracy.
result Asymptotically optimal in minimizing Bayes risk.
Optimizes electric field to control molecule states in Hartree-Fock theory.
problem Optimizing electric field to drive molecule from initial to target state.
method Trust region optimization with gradients from adjoint state method.
result Achieves desired target states with minimal control effort.
Improved confidence bounds for linear logistic model with applications to bandits.
problem Improving confidence bounds for linear logistic model.
method Self-concordant analysis of the logistic loss to avoid dependence on worst-case variance.
result Significant improvement in confidence bounds, avoiding dependence on 1 / κ 1/κ 1/ κ . Improved exploration in factored average-reward MDPs reduces regret.
problem Minimizing regret in unknown Factored Markov Decision Processes (FMDPs).
method DBN-UCRL strategy, inspired by UCRL2, uses Bernstein-type confidence sets for individual elements of the transition function.
result Achieves a regret bound with a leading term strictly improving over existing bounds.
Structured state space models improve ECG classification and reveal new insights.
problem Improving ECG analysis through deep learning.
method Applying structured state space models to capture long-term dependencies in ECG data.
result SSMs lead to significant improvements in ECG classification over current state-of-the-art.
Improves off-policy evaluation weights for balanced state-action pair distribution.
problem Imbalance in importance sampling weights for off-policy evaluation of contextual bandits.
method Balanced Off-Policy Evaluation (B-OPE) method that minimizes imbalance to desired counterfactual distribution of state-action pairs.
result Experimental evidence shows B-OPE improves offline policy evaluation in both discrete and continuous action spaces.
Paper introduces a new framework to improve sample efficiency in POMDPs learning.
problem Challenges in off-policy evaluation for POMDPs, especially with hidden states.
method Exploits the metric structure of belief space to relax coverage assumptions.
result Unified analysis technique yields tighter error bounds and sample efficiency improvements.
The paper proves a Wulff inequality for minimal submanifolds with boundary in Euclidean space.
problem Proving a Wulff inequality for minimal submanifolds with boundary.
method Associating a nonnegative anisotropic weight to the boundary of minimal submanifolds and proving the inequality.
result The Wulff inequality constant is independent of the weights and depends only on m m m and n n n . MinimalRNN simplifies RNNs for better interpretability and efficiency.
problem Improving interpretability and efficiency of RNNs.
method MinimalRNN uses a simplified structure with minimal updates, leading to efficient learning and testing.
result MinimalRNN learns disentangled RNN states and captures longer range dependencies.
The paper proves stability of certain graph types in Euclidean space with specific densities.
problem Stability of vertical and radial graphs in Euclidean space with certain densities.
method Techniques of calibrations used to prove stability and minimization.
result Vertical and radial graphs are strongly stable for specific densities.
The paper derives inequalities for contact CR-warped product submanifolds in cosymplectic space forms.
problem Establishing inequalities for contact CR-warped product submanifolds in cosymplectic space forms.
method Using the Gauss equation and hypotheses for cosymplectic and nearly cosymplectic manifolds, the paper derives inequalities for the norm of the second fundamental form and the shape operator.
result The contact warped product submanifolds in cosymplectic manifolds exhibit a geometric property called D 1 \mathcal{D}_1 D 1 -minimality, leading to an optimal general inequality. The paper tackles reward-relevance in offline RL with sparse decision dynamics.
problem Offline reinforcement learning with sparse decision dynamics and estimation sparsity.
method Reward-filtered least-squares policy evaluation using thresholded lasso.
result The method provides theoretical guarantees with sample complexity dependent on sparse component size.
Deep learning enhances active inference for dynamic state spaces.
problem Limited applicability of active inference to continuous state spaces.
method Use of deep learning to approximate probability distributions for active inference.
result Active inference can be applied to continuous state spaces.
We present a powerful general framework for designing data-dependent optimization algorithms, building upon and unifying recent techniques in adaptive regularization, optimistic gradient predictions, and problem-dependent randomization. We first present a series of new regret guarantees that hold at any time and under …
Algorithm reduces episode count for CMDPs with constraints.
problem Online decision-making with constraints in episodic CMDPs.
method Optimistic planning using linear programming for PAC guarantee.
result Probably approximately correct (PAC) guarantee on episode count.
The paper defines and characterizes conditional nonlinear expectations.
problem Defining and characterizing conditional nonlinear expectations.
method Embedding in decision theory, using state-dependent preferences, and continuous utility representation.
result Consistent backward conditional projections are characterized by the Sure-Thing Principle.
Study controlled contagion with state-dependent killing, proving a comparison principle.
problem Analyzing controlled McKean--Vlasov contagion with state-dependent killing.
method Proof of a comparison principle using Wasserstein smooth-gauge comparison and killing-jump absorption estimates.
result Established a comparison principle for the two-population killed-particle HJB.
The paper finds local minimizers for obstacle avoidance on curved spaces.
problem Finding optimal paths on curved spaces avoiding obstacles.
method Minimizing an action functional with bi-Jacobi fields and biconjugate points.
result Local minimizers are classified into two categories with local uniqueness results.
The paper uses Gaussian variational approximation for high-dimensional state space models.
problem High-dimensional state space models with complex covariance structures.
method Gaussian variational approximation with dynamic factor model for reduced covariance structure.
result The approach provides a reduced and conditional independence structure for high-dimensional state vectors.
In this paper, we propose a novel ranking framework for collaborative filtering with the overall aim of learning user preferences over items by minimizing a pairwise ranking loss. We show the minimization problem involves dependent random variables and provide a theoretical analysis by proving the consistency of the em…
The paper classifies stable free boundary minimal hypersurfaces outside a ball.
problem Classifying stable free boundary minimal hypersurfaces outside a ball.
method Proved a Bôcher type result for positive Jacobi functions and used a symmetrization procedure.
result Stable free boundary minimal hypersurfaces outside a ball are catenoidal.
Paper tackles offline SSP with value iteration for policy evaluation and learning.
problem Goal-oriented RL with offline data and cost minimization.
method Simple value iteration algorithms for OPE and offline policy learning.
result Strong instance-dependent bounds implying near-minimax optimal worst-case bounds.
AIF reformulated as convex MDP for adaptive behavior.
problem Adaptive behavior and policy optimization.
method Formulating AIF as convex MDP, deriving mirror descent algorithm.
result EFE minimization in AIF is equivalent to reward maximization in latent MDP, with epistemic component.
In this work we are interested in the problems of supervised learning and variable selection when the input-output dependence is described by a nonlinear function depending on a few variables. Our goal is to consider a sparse nonparametric model, hence avoiding linear or additive models. The key idea is to measure the …
Study geometric flows with varying parameters and prove continuous dependence.
problem Continuous dependence of flows on parameters in geometric settings.
method Derived suitable topologies for vector fields and flows, proved new continuous dependence.
result Proved continuous dependence of flows on parameters in a general topological space.
New model captures state-dependent variability in partially observed systems.
problem Structured stochasticity not captured by constant-variance models.
method State-coupled stochastic volatility framework with particle expectation-maximization.
result Model consistently reduces recovery bias under partial observation.
Study on regret minimization in deterministic MDPs.
problem Minimizing regret in deterministic reinforcement learning.
method Logarithmic regret lower bounds, leveraging graph theory and cycles.
result Explicitly quantifies the fundamental limit of performance achievable by any learning algorithm.
New algorithm for ML models in gradually adapting data settings.
problem Training models when data distribution reacts to the model over time.
method Stateful Performative Gradient Descent (Stateful PerfGD)
result Stateful PerfGD minimizes performative loss in gradually adapting data settings.
New SGMCMC method controls bias in SSMs for long time series.
problem Inference in SSMs is computationally prohibitive for long time series.
method Proposed new stochastic gradient estimators to control bias in SSMs.
result Developed novel SGMCMC samplers for various SSM types.
We consider nonparametric estimation of the state price density encapsulated in option prices. Unlike usual density estimation problems, we only observe option prices and their corresponding strike prices rather than samples from the state price density. We propose to model the state price density directly with a nonpa…
A submanifold M m M^m M m of a Euclidean space R m + p R^{m+p} R m + p is said to have harmonic mean curvature vector field if Δ H ⃗ = 0 Δ\vec{H}=0 Δ H = 0 , where H ⃗ \vec{H} H is the mean curvature vector field of M ↪ R m + p M\hookrightarrow R^{m+p} M ↪ R m + p and Δ Δ Δ is the rough Laplacian on M M M . There is a conjecture named after Bangyen Chen which states that submanifolds o…