Joongkyu Lee

Joongkyu Lee, Min-hwan Oh

We study optimal experimental design for multinomial logit (MNL) bandits, where an agent repeatedly selects a subset of $K$ items from a ground set of size $N$ and observes single-choice feedback. Unlike linear or generalized linear bandits, MNL bandits have a combinatorial action space, which makes classical optimal design approaches and naive optimization over all subsets computationally intractable. We propose a computationally efficient optimal design framework for MNL models that achieves both statistical efficiency and scalability through two complementary approaches: (i) an exact or certified-approximate reformulation of the design oracle as a $0$-$1$ mixed-integer linear program (MILP) with solver-certified early stopping, and (ii) a fully polynomial-time lifted design that replaces the nonlinear objective with a tractable surrogate. Using the Kiefer-Wolfowitz equivalence theorem, we establish near G-optimality guarantees and characterize the induced statistical-computational trade-offs. As an application, we develop a best assortment identification algorithm for MNL bandits with linear utilities and non-uniform revenues, and prove an instance-dependent sample complexity of $\tilde{O}\big(\frac{d \log N}{Δ^2}\big)$, where $d$ is the feature dimension, $N$ is the number of arms, and $Δ$ is the minimum revenue gap.

Joongkyu Lee, Min-hwan Oh

We study nonstationary generalized linear bandits (GLBs), where the expected reward is modeled through a nonlinear link function with an unknown time-varying parameter. This framework encompasses a broad class of reward models, including linear, Bernoulli, and binomial rewards. Existing approaches are predominantly based on maximum-likelihood estimation (MLE), using sliding-window, restart, or discounting mechanisms to handle nonstationarity. Although these methods achieve statistically efficient regret guarantees, they generally require revisiting past observations at every round, which leads to computation and memory costs that grow with time; moreover, several of them rely on a non-convex projection step. In this paper, we propose DOMD-GLB, a new algorithm for nonstationary GLBs that utilizes discounted online mirror descent (DOMD) for parameter estimation, thereby incurring only $O(1)$ computation and memory costs per round. We prove dynamic regret bounds of order $\tilde{O} \big(c_μ^{-1/2} d^{3/4} P_T^{1/4} T^{3/4}\big)$ in drifting environments and $\tilde{O}\big(c_μ^{-1/3} d^{2/3} Γ_T^{1/3} T^{2/3}\big) $in piecewise-stationary environments, where $d$ denotes the feature dimension, $T$ the time horizon, $P_T$ the path length, $Γ_T$ the number of change points, and $c_μ$ a curvature parameter associated with the link function, while substantially improving computational efficiency over prior work. To the best of our knowledge, this is the first algorithm for nonstationary GLBs with per-round computation and memory costs independent of time.

Deokgyu Yoon, Hyungkyu Kang, Joongkyu Lee et al.

Reinforcement learning with verifiable rewards (RLVR) plays a pivotal role in improving the reasoning ability of large language models. However, widely used PPO surrogate objectives are fundamentally local, as they rely on a local approximation of the exact policy gradient objective. While this approximation improves stability by reducing the variance induced by importance sampling, it also introduces structural bias into the surrogate objective, which must be controlled through trust region mechanisms. In this work, we introduce the $N$-step forward trace, which augments the PPO surrogate objective using the cumulative likelihood ratio of the next $N-1$ tokens. Building on this idea, we propose $N$-Step Forward-Trace Policy Optimization (NFPO), a practical RLVR algorithm that integrates the $N$-step forward trace into the masked policy gradient framework. NFPO provides a continuous bridge between the PPO surrogate objective and the exact policy gradient objective, offering a principled mechanism for controlling the bias-variance trade-off. Our theoretical analysis shows that, with an appropriate choice of $N$, the proposed objective yields a tighter policy-improvement bound than the standard PPO surrogate. Experiments on comprehensive reasoning benchmarks demonstrate that NFPO consistently improves performance, supporting our theoretical findings.

Heesang Ann, Joongkyu Lee, Min-hwan Oh

Vector quantization is a fundamental primitive for scalable machine learning systems, enabling memory-efficient storage, fast retrieval, and compressed inference. Recent rotation-based quantizers such as EDEN, RabitQ, and TurboQuant have introduced strong guarantees and empirical performance, but the surrounding comparisons have been difficult to interpret because they rely on different distortion criteria, probability regimes, and implementation assumptions. As our first contribution, we provide a unified theoretical comparison of these methods and show that their relative advantages are criterion-dependent rather than absolute: EDEN and TurboQuant are favorable for MSE distortion, EDEN is also effective for expected inner-product distortion, and RabitQ provides strong high-probability control. This comparison further clarifies that EDEN provides particularly strong guarantees for expected distortion measures. As our second contribution, we introduce Block-Sphere Quantization (BlockQuant), a new rotation-based block quantization algorithm designed around the spherical geometry of randomly rotated vectors. Unlike coordinate-wise quantizers, BlockQuant quantizes blocks on the sphere, preserving the geometry of rotated embeddings more faithfully. We prove that this block-spherical design theoretically improves over the baselines considered in this paper for both reconstruction MSE and expected inner-product distortion. Our experiments on real embedding datasets and long-context LLM inference tasks show practical gains that are consistent with our theoretical improvements.

Joongkyu Lee, Min-hwan Oh

In this paper, we study the contextual multinomial logit (MNL) bandit problem in which a learning agent sequentially selects an assortment based on contextual information, and user feedback follows an MNL choice model. There has been a significant discrepancy between lower and upper regret bounds, particularly regarding the maximum assortment size $K$. Additionally, the variation in reward structures between these bounds complicates the quest for optimality. Under uniform rewards, where all items have the same expected reward, we establish a regret lower bound of $Ω(d\sqrt{T/K})$ and propose a constant-time algorithm, OFU-MNL+, that achieves a matching upper bound of $\tilde{O}(d\sqrt{T/K})$. We also provide instance-dependent minimax regret bounds under uniform rewards. Under non-uniform rewards, we prove a lower bound of $Ω(d\sqrt{T})$ and an upper bound of $\tilde{O}(d\sqrt{T})$, also achievable by OFU-MNL+. Our empirical studies support these theoretical findings. To the best of our knowledge, this is the first work in the contextual MNL bandit literature to prove minimax optimality -- for either uniform or non-uniform reward setting -- and to propose a computationally efficient algorithm that achieves this optimality up to logarithmic factors.

Joongkyu Lee, Min-hwan Oh

In this work, we prove that, in linear MDPs, the feature dimension $d$ is lower bounded by $S/U$ in order to aptly represent transition probabilities, where $S$ is the size of the state space and $U$ is the maximum size of directly reachable states. Hence, $d$ can still scale with $S$ depending on the direct reachability of the environment. To address this limitation of linear MDPs, we propose a novel structural aggregation framework based on dynamics, named as the "dynamics aggregation". For this newly proposed framework, we design a provably efficient hierarchical reinforcement learning algorithm in linear function approximation that leverages aggregated sub-structures. Our proposed algorithm exhibits statistical efficiency, achieving a regret of $ \tilde{O} ( d_ψ^{3/2} H^{3/2}\sqrt{ N T} )$, where $d_ψ$ represents the feature dimension of aggregated subMDPs and $N$ signifies the number of aggregated subMDPs. We establish that the condition $d_ψ^3 N \ll d^{3}$ is readily met in most real-world environments with hierarchical structures, enabling a substantial improvement in the regret bound compared to LSVI-UCB, which enjoys a regret of $ \tilde{O} (d^{3/2} H^{3/2} \sqrt{ T})$. To the best of our knowledge, this work presents the first HRL algorithm with linear function approximation that offers provable guarantees.

Joongkyu Lee, Min-hwan Oh

In this paper, we propose an improved online confidence bound for multinomial logistic (MNL) models and apply this result to MNL bandits, achieving variance-dependent optimal regret. Recently, Lee & Oh (2024) established an online confidence bound for MNL models and achieved nearly minimax-optimal regret in MNL bandits. However, their results still depend on the norm-boundedness of the unknown parameter $B$ and the maximum size of possible outcomes $K$. To address this, we first derive an online confidence bound of $O\left(\sqrt{d \log t} + B \sqrt{d} \right)$, which is a significant improvement over the previous bound of $O (B \sqrt{d} \log t \log K )$ (Lee & Oh, 2024). This is mainly achieved by establishing tighter self-concordant properties of the MNL loss and applying Ville's inequality to bound the estimation error. Using this new online confidence bound, we propose a constant-time algorithm, OFU-MNL++, which achieves a variance-dependent regret bound of $O \Big( d \log T \sqrt{ \sum_{t=1}^T σ_t^2 } \Big) $ for sufficiently large $T$, where $σ_t^2$ denotes the variance of the rewards at round $t$, $d$ is the dimension of the contexts, and $T$ is the total number of rounds. Furthermore, we introduce a Maximum Likelihood Estimation (MLE)-based algorithm, OFU-MN$^2$L, which achieves an anytime poly(B)-free regret of $O \Big( d \log (BT) \sqrt{ \sum_{t=1}^T σ_t^2 } \Big) $.

Joongkyu Lee, Min-hwan Oh

In this paper, we consider combinatorial reinforcement learning with preference feedback, where a learning agent sequentially offers an action--an assortment of multiple items to--a user, whose preference feedback follows a multinomial logistic (MNL) model. This framework allows us to model real-world scenarios, particularly those involving long-term user engagement, such as in recommender systems and online advertising. However, this framework faces two main challenges: (1) the unknown value of each item, unlike traditional MNL bandits that only address single-step preference feedback, and (2) the difficulty of ensuring optimism while maintaining tractable assortment selection in the combinatorial action space with unknown values. In this paper, we assume a contextual MNL preference model, where the mean utilities are linear, and the value of each item is approximated by a general function. We propose an algorithm, MNL-VQL, that addresses these challenges, making it both computationally and statistically efficient. As a special case, for linear MDPs (with the MNL preference feedback), we establish the first regret lower bound in this framework and show that MNL-VQL achieves nearly minimax-optimal regret. To the best of our knowledge, this is the first work to provide statistical guarantees in combinatorial RL with preference feedback.

Joongkyu Lee, Seung Joon Park, Yunhao Tang et al.

In reinforcement learning, temporal abstraction in the action space, exemplified by action repetition, is a technique to facilitate policy learning through extended actions. However, a primary limitation in previous studies of action repetition is its potential to degrade performance, particularly when sub-optimal actions are repeated. This issue often negates the advantages of action repetition. To address this, we propose a novel algorithm named Uncertainty-aware Temporal Extension (UTE). UTE employs ensemble methods to accurately measure uncertainty during action extension. This feature allows policies to strategically choose between emphasizing exploration or adopting an uncertainty-averse approach, tailored to their specific needs. We demonstrate the effectiveness of UTE through experiments in Gridworld and Atari 2600 environments. Our findings show that UTE outperforms existing action repetition algorithms, effectively mitigating their inherent limitations and significantly enhancing policy learning efficiency.

Joongkyu Lee, Seouh-won Yi, Min-hwan Oh

We study online preference-based reinforcement learning (PbRL) with the goal of improving sample efficiency. While a growing body of theoretical work has emerged-motivated by PbRL's recent empirical success, particularly in aligning large language models (LLMs)-most existing studies focus only on pairwise comparisons. A few recent works (Zhu et al., 2023, Mukherjee et al., 2024, Thekumparampil et al., 2024) have explored using multiple comparisons and ranking feedback, but their performance guarantees fail to improve-and can even deteriorate-as the feedback length increases, despite the richer information available. To address this gap, we adopt the Plackett-Luce (PL) model for ranking feedback over action subsets and propose M-AUPO, an algorithm that selects multiple actions by maximizing the average uncertainty within the offered subset. We prove that M-AUPO achieves a suboptimality gap of $\tilde{O}\left( \frac{d}{T} \sqrt{ \sum_{t=1}^T \frac{1}{|S_t|}} \right)$, where $T$ is the total number of rounds, $d$ is the feature dimension, and $|S_t|$ is the size of the subset at round $t$. This result shows that larger subsets directly lead to improved performance and, notably, the bound avoids the exponential dependence on the unknown parameter's norm, which was a fundamental limitation in most previous works. Moreover, we establish a near-matching lower bound of $Ω\left( \frac{d}{K \sqrt{T}} \right)$, where $K$ is the maximum subset size. To the best of our knowledge, this is the first theoretical result in PbRL with ranking feedback that explicitly shows improved sample efficiency as a function of the subset size.