Paper tackles stochastic k k k -submodular bandits with full feedback, achieving sublinear regret.
problem Online optimization of k k k -submodular functions with full-bandit feedback. method Proposes online algorithms for various k k k -submodular stochastic combinatorial multi-armed bandit problems. result Achieves sublinear α α α -regret bounds for multiple k k k -submodular stochastic combinatorial multi-armed bandit problems. The paper tackles online learning problems with monotone arm sequences, achieving optimal or near-optimal regret bounds.
problem Online learning problems with ordinal and monotone arm sequences, such as dynamic pricing and clinical trials.
method Proposes algorithms for continuum-armed bandit problems with monotone arm sequences, achieving optimal or near-optimal regret bounds.
result Achieves optimal or near-optimal regret bounds for monotone arm sequences, differing from the continuous-armed bandit literature.
New framework tackles submodular welfare with multi-agent combinatorial bandits.
problem Maximizing total welfare among agents with shared constraints and submodular utilities under bandit feedback.
method Proposes an explore-then-commit strategy with randomized assignments for multi-agent combinatorial bandits.
result Achieves i l d e O ( T 2 / 3 ) ilde{\mathcal{O}}(T^{2/3}) i l d e O ( T 2/3 ) regret, first for partition-based submodular welfare problem under bandit feedback. Graph-Triggered Bandits unify rested and restless bandits with graph-defined arm interactions.
problem Modeling sequential decision-making problems with evolving arm rewards.
method Graph-Triggered Bandits (GTBs) framework that generalizes rested and restless bandits using a graph.
result Rested and restless bandits are special cases of GTBs for suitable graphs.
Adaptive learning rate improves FTRL's performance in online learning.
problem Optimizing FTRL's learning rate for competitive regret in online learning.
method Formulated as a sequential decision-making problem, introduced competitive analysis framework, and proposed stability-penalty matching update rules.
result Achieved a constant competitive ratio under specific conditions, enabling Best-Of-Both-Worlds algorithms.
Investigates probability of error in structured thresholding bandit problems.
problem Probability of misclassifying arms in structured thresholding bandit problems.
method Analyzes two shape constraints: monotonic increasing and concave sequences of arm means.
result Upper and lower bounds for the probability of error match up to constants in the problem dependent regime.
New insights on bias in multi-armed bandits under conditional sampling.
problem Understanding bias in multi-armed bandits under conditional sampling.
method Characterized the sign of conditional bias of monotone functions of rewards.
result Sign of conditional bias can differ from marginal bias, depending on conditioning events.
New lower bounds for combinatorial multi-armed bandits for general reward functions.
problem Maximizing reward in sequential decisions with sets of arms.
method Proved tight regret lower bounds for all smooth reward functions under mild assumptions.
result Lower bounds are tight up to log-factors for monotone reward functions.
Paper tackles non-monotonic resource utilization in sequential decision-making.
problem Sequential decision-making under uncertainty with resource constraints.
method Introduces a new MDP policy with constant regret against LP relaxation.
result Develops a learning algorithm with logarithmic regret for unknown outcome distributions.
New algorithms reduce regret in non-stationary bandits with increasing payoffs.
problem Non-stationary bandits with monotonically increasing payoffs.
method R-ed-UCB for rested case and R-less-UCB for restless case.
result Regret bound of O ~ ( T 2 3 ) \widetilde{\mathcal{O}}(T^{\frac{2}{3}}) O ( T 3 2 ) under certain conditions. New algorithm reduces regret for single-index bandits to nearly optimal.
problem Optimizing rewards from unknown projections of high-dimensional contexts.
method Two-phase algorithm: estimate projection direction, reduce to 1D bandit, use UCB.
result Achieved optimal regret of i l d e O ( T 2 / 3 ) ilde{\mathcal{O}}(T^{2/3}) i l d e O ( T 2/3 ) . Improved regret for single-index bandits with optimal algorithm.
problem Optimizing rewards from unknown one-dimensional projections of high-dimensional contexts.
method Two-phase algorithm: first estimate projection direction, then discretize and use UCB.
result Achieved optimal regret of i l d e O ( T 2 / 3 ) ilde{\mathcal{O}}(T^{2/3}) i l d e O ( T 2/3 ) . New algorithms for generalized linear bandits with unknown reward functions.
problem Misspecification of reward functions in existing bandit algorithms.
method Introducing single index bandits, proposing STOR, ESTOR, and GSTOR algorithms.
result Achieved nearly optimal regret bound of i l d e O T ( T ) ilde{O}_T(\sqrt{T}) i l d e O T ( T ) . 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.
New algorithm reduces reinforcement learning complexity, approaching contextual bandits.
problem Episodic reinforcement learning's difficulty compared to contextual bandits.
method Proposes MVP algorithm with a new Bernstein-type bonus for episodic reinforcement learning.
result Achieves near-optimal regret bound of $O\left(\left(\sqrt{SAK} + S^2A
ight) \poly\log \left(SAHK
ight)
ight)$ , improving state-of-the-art results.
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. Self-referential meta learning avoids explicit optimization by modifying itself.
problem Dependency on human engineering in meta learning algorithms.
method Investigates self-referential meta learning systems that modify themselves without explicit optimization.
result Self-referential neural networks can improve their own modifications without explicit optimization.
The paper studies how arm selection in a bandit problem changes with shape constraints.
problem Stochastic Thresholding Bandit Problem under shape constraints.
method Investigation of TBP under four shape constraints: monotonic increasing, unimodal, concave, and fixed.
result Minimax rates for regret vary significantly depending on the shape constraint.
The paper tackles rested bandits with non-decreasing and concave rewards, deriving lower bounds and an efficient algorithm.
problem Studying the sample complexity and optimal strategies for rested bandits with specific reward properties.
method Deriving regret lower bounds and designing an efficient algorithm R-ed-UCB with theoretical and empirical analysis.
result An efficient algorithm R-ed-UCB with a regret bound of O ~ ( T 2 3 ) \widetilde{\mathcal{O}}(T^{\frac{2}{3}}) O ( T 3 2 ) under certain conditions. Study best arm identification with safety constraints in bandit problems.
problem Real-world decision-making with safety constraints.
method Analyzed linear and monotonic reward and safety constraints, proposed algorithms.
result Guaranteed safe learning in both linear and general reward/safety constraint settings.
New framework for decentralized optimization of upper-linearizable functions with improved regret and complexity.
problem Decentralized optimization of upper-linearizable functions with general constraints.
method Decentralized projection-free optimization with upper-linearizable function framework.
result Regret of O ( T 1 − θ / 2 ) O(T^{1-θ/2}) O ( T 1 − θ /2 ) with communication complexity of O ( T θ ) O(T^θ) O ( T θ ) and linear optimization calls of O ( T 2 θ ) O(T^{2θ}) O ( T 2 θ ) . We analyze the sample complexity of the thresholding bandit problem, with and without the assumption that the mean values of the arms are increasing. In each case, we provide a lower bound valid for any risk δ δ δ and any δ δ δ -correct algorithm; in addition, we propose an algorithm whose sample complexity is of the same o…
New algorithm models satiation in recommender systems.
problem Satiation effects in user preferences not modeled by existing algorithms.
method Rebounding bandits, modeling satiation as time-invariant linear dynamical systems.
result Greedy policy optimal for identical deterministic dynamics; EEP algorithm for stochastic dynamics.
Paper proposes DG-ETC for online submodular maximization with stochastic bandit feedback.
problem Online unconstrained submodular maximization with stochastic bandit feedback.
method Double-Greedy - Explore-then-Commit (DG-ETC) approach.
result DG-ETC achieves logarithmic regret O ( d log ( d T ) ) O(d\log(dT)) O ( d log ( d T )) for 1 / 2 1/2 1/2 -approximate pseudo-regret. Optimizes profit in targeted marketing across multiple markets with varying marketing expenditures.
problem Maximizing profit in a sequential marketing strategy with multiple markets and varying marketing costs.
method Near-optimal algorithms in an adversarial bandit setting, proving regret bounds for different demand curve types.
result Proved near-optimal regret bounds for the profit-maximization problem in targeted marketing.
Bandit algorithms have been predominantly analyzed in the convex setting with function-value based stationary regret as the performance measure. In this paper, motivated by online reinforcement learning problems, we propose and analyze bandit algorithms for both general and structured nonconvex problems with nonstation…
New algorithm for combinatorial bandit problems reduces regret.
problem Optimal selection of sets of arms in bandit problems.
method SGB algorithm with optimized exploration of unselected arms.
result Achieves ( 1 − 1 / e ) (1-1/e) ( 1 − 1/ e ) -regret bound of O ( n 1 3 k 2 3 T 2 3 log ( T ) 2 3 ) \mathcal{O}(n^{\frac{1}{3}} k^{\frac{2}{3}} T^{\frac{2}{3}} \log(T)^{\frac{2}{3}}) O ( n 3 1 k 3 2 T 3 2 log ( T ) 3 2 ) . New algorithms improve performance guarantees for multi-armed bandits problems.
problem Allocating effort under uncertainty in scenarios like investing research effort.
method Proposed two new families of bandit algorithms with stronger guarantees.
result Achieved optimal dependence on k with additional properties of arm reward curves.
New algorithm for competing influence spread in unknown networks.
problem Maximizing influence spread in a social network with unknown probabilities.
method Combinatorial multi-armed bandit (CMAB) framework, Triggering Probability Modulated (TPM) condition, OCIM-TS, OCIM-OFU, OCIM-ETC.
result Sublinear Bayesian and frequentist regret for OCIM-TS and OCIM-OFU, respectively.
We study the problem of finding the optimal dosage in early stage clinical trials through the multi-armed bandit lens. We advocate the use of the Thompson Sampling principle, a flexible algorithm that can accommodate different types of monotonicity assumptions on the toxicity and efficacy of the doses. For the simplest…
Improved guarantees for misspecified kernelized bandit optimization.
problem Misspecification in kernelized bandit optimization.
method Localization and domain splitting techniques.
result Logarithmic or polylogarithmic growth of misspecification amplification.
This paper introduces a new metric, ULI, for RL that ensures both cumulative and instantaneous performance.
problem High-stakes applications require RL algorithms to avoid playing bad policies.
method Introduces uniform last-iterate (ULI) guarantee, a stronger metric capturing both cumulative and instantaneous performance.
result ULI directly implies near-optimal cumulative performance across various metrics, but not the other way around.
It is well known that in stochastic multi-armed bandits (MAB), the sample mean of an arm is typically not an unbiased estimator of its true mean. In this paper, we decouple three different sources of this selection bias: adaptive \emph{sampling} of arms, adaptive \emph{stopping} of the experiment, and adaptively \emph{…
New algorithm reduces submodular maximization regret to nearly optimal bounds.
problem Maximizing submodular functions under stochastic bandit feedback with cardinality constraint.
method Sub-UCB algorithm, robust greedy approximation, minimax lower bounds.
result Achieves nearly optimal regret bounds for submodular maximization.
Transforms offline greedy algorithms to online algorithms for combinatorial problems.
problem Online decision-making in time-varying combinatorial environments.
method General framework using Blackwell approachability and Bandit Blackwell approachability.
result Achieves O ( T ) O(\sqrt{T}) O ( T ) regret in full information setting and O ( T 2 / 3 ) O(T^{2/3}) O ( T 2/3 ) regret in bandit setting. New decision support systems use prediction sets to help experts update their predictions, improving performance.
problem Challenges in explaining and updating predictions from decision support systems.
method Developed a methodology leveraging nested structure of prediction sets and counterfactual monotonicity to improve performance.
result Limiting experts' agency leads to better performance in decision support systems based on prediction sets.
New insights on eluder dimension for function approximation in machine learning.
problem Complexity measure for online bandits and reinforcement learning with function approximation.
method Study the relationship between eluder dimension and generalized rank for different activation functions.
result Eluder dimension can be exponentially smaller or larger than generalized rank depending on the activation function.
Study best arm identification in restless Markov multi-armed bandits with state-dependent transitions.
problem Identify the best arm in a multi-armed bandit with time-varying states.
method Propose a sequential policy to select arms without knowing their exact TPMs.
result Upper and lower bounds on expected time to find the best arm match in a special case.
The paper addresses monotonicity in machine learning models for fairness and accountability.
problem Ensuring fairness and accountability in transparent machine learning models.
method Study of three types of monotonicity (individual, weak pairwise, strong pairwise) and propose monotonic groves of neural additive models.
result Monotonic groves of neural additive models maintain transparency, accountability, and fairness.
New framework handles online decisions with replenishable resources, improving both adversarial and stochastic performance.
problem Online decision-making with resource constraints that can be replenished.
method Best-of-both-worlds primal-dual template for online learning problems with replenishment.
result First positive results for adversarial inputs and an instance-independent regret bound for stochastic inputs.
The paper tackles resource allocation for arms with unknown and random rewards, achieving optimal regret bounds.
problem Allocating resources on arms with unknown and random rewards.
method Developed two algorithms with optimal regret bounds for b ∈ [ 0 , 1 ] b \in [0,1] b ∈ [ 0 , 1 ] , demonstrating a phase transition at b = 1 / 2 b=1/2 b = 1/2 . result Achieved optimal gap-dependent and gap-independent regret bounds for b ∈ [ 0 , 1 ] b \in [0,1] b ∈ [ 0 , 1 ] . Probit Monotone BART estimates binary outcomes using monotonic functions.
problem Estimating conditional mean functions for binary outcomes with monotonicity constraints.
method Proposes a new BART variant that incorporates monotonicity constraints for binary outcomes.
result Allows for more precise estimation of monotonic functions in binary outcome models.
Boltzmann exploration is a classic strategy for sequential decision-making under uncertainty, and is one of the most standard tools in Reinforcement Learning (RL). Despite its widespread use, there is virtually no theoretical understanding about the limitations or the actual benefits of this exploration scheme. Does it…
Monotone neural networks can approximate and interpolate functions efficiently.
problem Understanding the efficiency and expressiveness of monotone neural networks.
method Solving the monotone interpolation problem using depth-4 networks and comparing size bounds with arbitrary networks.
result Monotone neural networks can approximate and interpolate functions efficiently, but may require exponential size in high dimensions.
Improves k-NN for monotonic data with robustness against noise.
problem Class noise in real-life data violates monotonic constraints in k-NN.
method Monotonic Fuzzy k-NN (MonFkNN) with new fuzzy membership calculation.
result Significant accuracy improvements and robustness against monotonic noise.
Study examines explainable machine learning for monotonic models, finding Integrated gradients better for strong monotonicity.
problem Applying explainable machine learning to science-informed models.
method Proposed axioms for monotonicity, tested Shapley value and Integrated gradients methods.
result Integrated gradients provides better explanations for strong monotonicity.
Formula proves monotonicity for anisotropic minimal hypersurfaces.
problem Understanding anisotropic minimal hypersurfaces.
method Proved a monotonicity formula under a sign assumption on the Minkowski norm.
result Monotonicity formula for anisotropic minimal hypersurfaces.
New example of manifolds with monotonic heat kernels found.
problem Understanding monotonicity of heat kernels on manifolds.
method Analyzing new examples and classifying flat tori.
result Generic metrics fail monotonicity at large times.