Study optimizes dynamic product selection and pricing using censored preference feedback.
problem Maximizing revenue from dynamic assortment and pricing decisions.
method Proposes a censored multinomial logit model and LCB pricing strategy combined with UCB or TS product selection.
result Achieves optimal regret bounds for dynamic pricing and selection.
New RL method tackles dynamic MDPs with evolving rewards and states.
problem Dynamic MDPs with evolving rewards and states.
method Sliding Window Upper-Confidence bound for Reinforcement Learning (SWUCRL2-CW) and Bandit-over-Reinforcement Learning (BORL).
result Achieves dynamic regret bound for non-stationary MDPs.
LqgOpt learns optimal control in unknown LQG systems with minimal regret.
problem Adaptive control in partially observable linear quadratic Gaussian systems with unknown dynamics.
method Optimism in the face of uncertainty, predictor state evolution, closed-loop system identification, confidence bounds.
result Proves a regret upper bound of i l d e O ( T ) ilde{\mathcal{O}}(\sqrt{T}) i l d e O ( T ) for LQG systems. We propose an algorithm combining calibrated prediction and generalization bounds from learning theory to construct confidence sets for deep neural networks with PAC guarantees---i.e., the confidence set for a given input contains the true label with high probability. We demonstrate how our approach can be used to cons…
New algorithm optimizes online decision-making with dynamically generated actions.
problem Balancing action generation costs with optimal decision-making in online learning.
method Doubly-optimistic algorithm using LCB for action selection and UCB for action generation.
result Achieves optimal regret bound of O ( T d d + 2 d d d + 2 + d T log T ) O(T^{\frac{d}{d+2}}d^{\frac{d}{d+2}} + d\sqrt{T\log T}) O ( T d + 2 d d d + 2 d + d T log T ) . Paper tackles dynamic assortment with dual contexts, improving revenue in e-commerce.
problem Maximizing revenue in e-commerce with personalized recommendations from vast catalogs.
method Low-rank dynamic assortment model and upper confidence bound approach.
result Regret bound of i l d e O ( ( d 1 + d 2 ) r T ) ilde{O}((d_1+d_2)r\sqrt{T}) i l d e O (( d 1 + d 2 ) r T ) for dynamic assortment problem. We consider un-discounted reinforcement learning (RL) in Markov decision processes (MDPs) under temporal drifts, ie, both the reward and state transition distributions are allowed to evolve over time, as long as their respective total variations, quantified by suitable metrics, do not exceed certain variation budgets. …
The SPS method constructs confidence regions for true parameters with optimal sample complexity.
problem Constructing exact, non-asymptotic confidence regions for true system parameters.
method Sign-Perturbed Sums (SPS) method, generalized to various types of problems.
result High probability upper bounds for SPS confidence regions show optimal shrinkage rate.
A hybrid model for Bayesian optimization handles mixed variables using MCTS for categorical and GP for continuous.
problem Optimizing functions with mixed variable types (continuous, integer, categorical).
method Merges MCTS for categorical and GP for continuous variables, integrates UCTS search strategy, and dynamically selects kernels.
result Hybrid models outperform traditional methods in Bayesian optimization.
New method for linear bandits with unknown sparsity, improving sparse regret bounds.
problem Sparse regret bounds for unknown sparsity and adversarial action sets.
method Combines online to confidence set conversions with randomized model selection over nested confidence sets.
result First sparse regret bounds for unknown sparsity and adversarial action sets.
PAC-MCTS addresses biased search in LLM-guided planning by dynamically pruning.
problem Systematic biases in LLMs lead to inefficient and unsafe search in deep planning tasks.
method Formulates node expansion as BAI under bounded bias, derives sample complexity bounds, and proposes PAC-MCTS for dynamic confidence bounds.
result PAC-MCTS improves robustness and efficiency by up to 78% fewer API evaluations and 3x higher sample efficiency.
New tighter confidence bounds for sequential kernel regression.
problem Quantifying uncertainty in sequential learning algorithms.
method Martingale tail inequalities and conic programming.
result New confidence bounds are tighter than existing ones.
Study optimal control in unknown nonlinear systems with near-optimal regret bound.
problem Sequential control in unknown, nonlinear dynamical systems.
method LC^3 algorithm, based on information theory.
result Near-optimal O ( T ) O(\sqrt{T}) O ( T ) regret bound for episodic settings. Optimal strategy for reinforcement learning with delayed observations.
problem Delayed state observation in reinforcement learning.
method Combines augmentation method and upper confidence bound approach.
result Minimax optimal regret bound of i l d e O ( H D max S A K ) ilde{\mathcal{O}}(H \sqrt{D_{\max} SAK}) i l d e O ( H D m a x S A K ) . In this paper we introduce a deep learning method for pricing and hedging American-style options. It first computes a candidate optimal stopping policy. From there it derives a lower bound for the price. Then it calculates an upper bound, a point estimate and confidence intervals. Finally, it constructs an approximate …
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.
New algorithm tackles non-stationary reinforcement learning with general function approximation.
problem Understanding non-stationary MDPs with function approximation.
method Dynamic Bellman Eluder (DBE) dimension for complexity, sliding window mechanism, confidence set design.
result Upper bound on dynamic regret for proposed SW-OPEA algorithm.
A new differentiable UCB algorithm for linear bandits learns adaptive confidence bounds.
problem Inability of UCB to strike optimal exploration-exploitation due to confidence bounds.
method Proposes a differentiable linear bandit algorithm and a gradient estimator for learning adaptive confidence bounds.
result Achieves a i l d e O ( β ^ d T ) ilde{\mathcal{O}}(\hatβ\sqrt{dT}) i l d e O ( β ^ d T ) upper bound of T T T -round regret. This paper analyzes the multi-armed bandit problem using frequency-domain methods.
problem The exploration-exploitation trade-off in sequential decision-making.
method Proposes a frequency-domain analysis framework, reformulating the bandit process as a signal processing problem.
result Confidence bound term in UCB algorithm is equivalent to a time-varying gain in frequency domain.
This work uses variational inference to estimate parameters of opinion dynamics models.
problem Challenges in parameter estimation for ABMs of social phenomena.
method Transformed ABM parameter estimation into an optimization problem using variational inference.
result Estimates parameters more accurately than simulation-based and MCMC methods.
The paper honors Lai's contributions to multi-armed bandits and establishes new regret bounds.
problem Improving regret bounds in multi-armed bandit problems.
method Establishes non-asymptotic regret bounds for upper confidence bound indices.
result New regret bounds match Lai-Robbins lower bound.
Adapts model-based advice to stabilize black-box policies for nonlinear control.
problem Stabilizing machine-learned policies for nonlinear control with limited model information.
method Proposes an adaptive λ λ λ -confident policy to combine black-box and model-based advice. result Proves the stability of the adaptive λ λ λ -confident policy and its competitive ratio. The paper extends confidence sequences for infinite variance data.
problem Addressing confidence sequences for distributions with infinite variance.
method Establishing lower bounds and deriving tight confidence sequences for relaxed bounded p t h p^{th} p t h -moment distributions. result Derived confidence sequences are tighter than those using Dubins-Savage inequality.
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 . Research aims to improve confidence intervals for RKHS elements in online learning.
problem Improper confidence intervals lead to suboptimal regret bounds in kernel-based bandit and reinforcement learning.
method Formalizes the open problem of online confidence intervals in RKHS and reviews existing results.
result Identifies the online nature of observation points as the main challenge for tight confidence intervals.
Develops hypothesis tests for conditional distributions using learning-theoretic bounds.
problem Testing differences in conditional distributions and functionals.
method Transforming learning-theoretic bounds into hypothesis tests for conditional expectations.
result Establishes comprehensive foundation for conditional testing, including theoretical guarantees and practical implementations.
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. Near-optimal confidence intervals for bounded data.
problem Online inference for sequential decision problems like A/B testing.
method Utilizing Bentkus' concentration results to improve on existing methods.
result Near-optimal confidence intervals confirmed favorable in synthetic and practical applications.
A new framework tightens risk measure confidence bounds.
problem Improving confidence bounds for various risk measures.
method Distribution optimization framework with two estimation schemes based on concentration bounds.
result Consistently tighter confidence bounds compared to previous methods.
New framework handles dynamic contexts in reinforcement learning.
problem Learning in environments where contexts change over time.
method Dynamic Contextual Markov Decision Processes (DCMDPs) with logistic aggregation.
result Upper-confidence-bound style algorithm with regret bounds.
Note improves confidence bounds for random variables.
problem Improving confidence bounds for random variables with unbounded ranges and different distributions.
method PAC-Bayes-ification of a derived confidence bound.
result Streamlined proofs for existing results.
The design of personalized incentives or recommendations to improve user engagement is gaining prominence as digital platform providers continually emerge. We propose a multi-armed bandit framework for matching incentives to users, whose preferences are unknown a priori and evolving dynamically in time, in a resource c…
Paper presents a privacy-preserving method for dynamic assortment selection.
problem Personalized assortment recommendations with data privacy concerns.
method Perturbed upper confidence bound method integrating calibrated noise.
result Policy satisfies Joint Differential Privacy (JDP) with near-optimal regret bound.
Safe learning of stochastic dynamics with safety constraints.
problem Learning controlled stochastic dynamics with safety constraints.
method Iterative expansion of a safe control set using kernel-based confidence bounds.
result The method ensures safe exploration and efficient estimation of system dynamics.
Improved algorithms for stochastic linear bandits using tighter confidence sequences.
problem Stochastic linear bandits with improved worst-case regret guarantees.
method Novel tail bound for adaptive martingale mixtures to construct tighter confidence sequences.
result Linear bandit algorithm achieves competitive worst-case regret.
Paper presents robust confidence sequences for means with known moment bounds and arbitrary corruption.
problem Tackles robustness to outliers and adversarial corruptions in mean estimation.
method Designs new robust exponential supermartingales to create confidence sequences.
result Achieves optimal width and shows smaller margin of error compared to fixed-time robust methods.
The paper finds a fundamental trade-off between confidence and efficiency in transductive conformal prediction.
problem The challenge is to balance confidence and efficiency in predicting multiple data points.
method The authors derive a strict finite-sample bound and introduce a practical algorithm to approach this bound.
result Any non-trivial confidence level leads to exponential growth in prediction set size, with a linear scaling in the number of samples.
This paper improves GP-UCB by using a shifted exponential distribution for confidence parameters.
problem Theoretical confidence parameter in GP-UCB increases with iterations, leading to large values.
method Introduced IRGP-UCB, a randomized variant of GP-UCB using a shifted exponential distribution for confidence parameters.
result IRGP-UCB achieves sub-linear regret without increasing the confidence parameter.
Improved online confidence bounds for multinomial logistic models in bandits.
problem Achieving optimal regret in multinomial logistic bandits with bounded parameters and outcomes.
method Deriving an improved online confidence bound and proposing OFU-MNL++ and OFU-MN 2 ^2 2 L algorithms. result Achieved variance-dependent optimal regret for MNL bandits.
The paper presents a method to compute trusted confidence bounds for LECs in CPS.
problem Non-transparent predictions of LECs make CPS safety challenging.
method Inductive Conformal Prediction (ICP) and Triplet Network architecture.
result Efficient real-time computation of trusted confidence bounds.
Develops confidence bounds for off-policy evaluation in contextual bandits.
problem Evaluating policies that were not used to collect data.
method Martingale analysis for non-asymptotic, non-parametric, and valid confidence sequences.
result Empirically tight bounds on failure probability and width.
We develop algorithms with low regret for learning episodic Markov decision processes based on kernel approximation techniques. The algorithms are based on both the Upper Confidence Bound (UCB) as well as Posterior or Thompson Sampling (PSRL) philosophies, and work in the general setting of continuous state and action …
In the field of reinforcement learning there has been recent progress towards safety and high-confidence bounds on policy performance. However, to our knowledge, no practical methods exist for determining high-confidence policy performance bounds in the inverse reinforcement learning setting---where the true reward fun…
Entropy rate of sequential data-streams naturally quantifies the complexity of the generative process. Thus entropy rate fluctuations could be used as a tool to recognize dynamical perturbations in signal sources, and could potentially be carried out without explicit background noise characterization. However, state of…
The paper improves confidence regions for band-limited functions using tighter norm bounds and majority voting.
problem Constructing reliable confidence regions for band-limited functions from noisy data.
method Improved norm bounds using Hoeffding's inequality and empirical Bernstein bound, majority voting to aggregate intervals.
result Confidence intervals retain their simultaneous coverage guarantee even when aggregated from random subsamples.
Paper improves confidence intervals and variance estimation for deep learning models.
problem Improving confidence intervals and variance estimation in deep learning models.
method Residual-based framework for conditional variance estimation; robust bootstrap procedure for confidence intervals.
result First non-asymptotic bounds for variance estimation using ReLU networks.
The estimation of probabilities of default (PDs) for low default portfolios by means of upper confidence bounds is a well established procedure in many financial institutions. However, there are often discussions within the institutions or between institutions and supervisors about which confidence level to use for the…
We provide a pointwise confidence bound for non-linear least-squares with fixed design.
problem Confidence estimation in non-linear ℓ 2 \ell^2 ℓ 2 -regularized least squares. method Pointwise confidence bound for local minimizers, using weighted norm involving inverse-Hessian.
result The proposed confidence bound scales with the test input's similarity to the training data.