Kevin Tan

Chinmaya Kausik, Yangyi Lu, Kevin Tan et al.

Evaluating and optimizing policies in the presence of unobserved confounders is a problem of growing interest in offline reinforcement learning. Using conventional methods for offline RL in the presence of confounding can not only lead to poor decisions and poor policies, but also have disastrous effects in critical applications such as healthcare and education. We map out the landscape of offline policy evaluation for confounded MDPs, distinguishing assumptions on confounding based on whether they are memoryless and on their effect on the data-collection policies. We characterize settings where consistent value estimates are provably not achievable, and provide algorithms with guarantees to instead estimate lower bounds on the value. When consistent estimates are achievable, we provide algorithms for value estimation with sample complexity guarantees. We also present new algorithms for offline policy improvement and prove local convergence guarantees. Finally, we experimentally evaluate our algorithms on both a gridworld environment and a simulated healthcare setting of managing sepsis patients. In gridworld, our model-based method provides tighter lower bounds than existing methods, while in the sepsis simulator, our methods significantly outperform confounder-oblivious benchmarks.

Chinmaya Kausik, Kevin Tan, Ambuj Tewari

We present an algorithm for learning mixtures of Markov chains and Markov decision processes (MDPs) from short unlabeled trajectories. Specifically, our method handles mixtures of Markov chains with optional control input by going through a multi-step process, involving (1) a subspace estimation step, (2) spectral clustering of trajectories using "pairwise distance estimators," along with refinement using the EM algorithm, (3) a model estimation step, and (4) a classification step for predicting labels of new trajectories. We provide end-to-end performance guarantees, where we only explicitly require the length of trajectories to be linear in the number of states and the number of trajectories to be linear in a mixing time parameter. Experimental results support these guarantees, where we attain 96.6% average accuracy on a mixture of two MDPs in gridworld, outperforming the EM algorithm with random initialization (73.2% average accuracy).

Joseph H. Rudoler, Kevin Tan, Giles Hooker et al.

Deep learning systems are known to exhibit implicit regularization (alt. implicit bias), favoring simple solutions instead of merely minimizing the loss function. In some cases, we can analytically derive the implicit regularization -- connecting it to an equivalent penalty that augments the learning objective. However, modern deep learning systems are complex, carrying modifications to the training procedure and architecture (e.g. early stopping, minibatching, dropout) whose effects are not always directly interpretable. Although estimating the resulting implicit regularization could aid theorists in algorithm design and practitioners in interpreting their hyperparameter choices, this problem has received little direct attention. It is also tractable: regularization makes weight updates deviate from loss gradients, promising a signal for identifying implicit bias. Here we provide gradient matching methods that can be used to empirically estimate the implicit regularization. Our method works on networks with known regularization, recovering popular explicit penalties like $\ell_1$ and $\ell_2$. It also replicates known implicit effects, like the quadratic weight penalty induced by early stopping in gradient descent, demonstrating that it can be used to test theories of implicit regularization. Crucially, because our method is empirical, it can handle implicit regularization in arbitrary networks. We demonstrate this use by characterizing the effects of dropout in deep networks, showing implicit $\ell_2$ effects in this popular method. Our work shows that practitioners can use gradient matching to understand regularization in networks with implicit biases that are too complicated to derive analytically.

Max Qiushi Lin, Reza Asad, Kevin Tan et al.

Although actor-critic methods have been successful in practice, their theoretical analyses have several limitations. Specifically, existing theoretical work either sidesteps the exploration problem by making strong assumptions or analyzes impractical methods with complicated algorithmic modifications. Moreover, the actor-critic methods analyzed for linear MDPs often employ natural policy gradient (NPG) and construct "implicit" policies without explicit parameterization. Such policies are computationally expensive to sample from, making the environment interactions inefficient. To that end, we focus on the finite-horizon linear MDPs and propose an optimistic actor-critic framework that uses parametric log-linear policies. In particular, we introduce a tractable \textit{logit-matching} regression objective for the actor. For the critic, we use approximate Thompson sampling via Langevin Monte Carlo to obtain optimistic value estimates. We prove that the resulting algorithm achieves $\widetilde{\mathcal{O}}(ε^{-4})$ and $\widetilde{\mathcal{O}}(ε^{-2})$ sample complexity in the on-policy and off-policy setting, respectively. Our results match prior theoretical works in achieving the state-of-the-art sample complexity, while our algorithm is more aligned with practice.

Kevin Tan, Wei Fan, Yuting Wei

Hybrid Reinforcement Learning (RL), where an agent learns from both an offline dataset and online explorations in an unknown environment, has garnered significant recent interest. A crucial question posed by Xie et al. (2022) is whether hybrid RL can improve upon the existing lower bounds established in purely offline and purely online RL without relying on the single-policy concentrability assumption. While Li et al. (2023) provided an affirmative answer to this question in the tabular PAC RL case, the question remains unsettled for both the regret-minimizing RL case and the non-tabular case. In this work, building upon recent advancements in offline RL and reward-agnostic exploration, we develop computationally efficient algorithms for both PAC and regret-minimizing RL with linear function approximation, without single-policy concentrability. We demonstrate that these algorithms achieve sharper error or regret bounds that are no worse than, and can improve on, the optimal sample complexity in offline RL (the first algorithm, for PAC RL) and online RL (the second algorithm, for regret-minimizing RL) in linear Markov decision processes (MDPs), regardless of the quality of the behavior policy. To our knowledge, this work establishes the tightest theoretical guarantees currently available for hybrid RL in linear MDPs.

Kevin Tan, Ziping Xu

Hybrid Reinforcement Learning (RL), leveraging both online and offline data, has garnered recent interest, yet research on its provable benefits remains sparse. Additionally, many existing hybrid RL algorithms (Song et al., 2023; Nakamoto et al., 2023; Amortila et al., 2024) impose coverage assumptions on the offline dataset, but we show that this is unnecessary. A well-designed online algorithm should "fill in the gaps" in the offline dataset, exploring states and actions that the behavior policy did not explore. Unlike previous approaches that focus on estimating the offline data distribution to guide online exploration (Li et al., 2023b), we show that a natural extension to standard optimistic online algorithms -- warm-starting them by including the offline dataset in the experience replay buffer -- achieves similar provable gains from hybrid data even when the offline dataset does not have single-policy concentrability. We accomplish this by partitioning the state-action space into two, bounding the regret on each partition through an offline and an online complexity measure, and showing that the regret of this hybrid RL algorithm can be characterized by the best partition -- despite the algorithm not knowing the partition itself. As an example, we propose DISC-GOLF, a modification of an existing optimistic online algorithm with general function approximation called GOLF used in Jin et al. (2021); Xie et al. (2022a), and show that it demonstrates provable gains over both online-only and offline-only reinforcement learning, with competitive bounds when specialized to the tabular, linear and block MDP cases. Numerical simulations further validate our theory that hybrid data facilitates more efficient exploration, supporting the potential of hybrid RL in various scenarios.

Kevin Tan, Wei Fan, Yuting Wei

Actor-critic algorithms have become a cornerstone in reinforcement learning (RL), leveraging the strengths of both policy-based and value-based methods. Despite recent progress in understanding their statistical efficiency, no existing work has successfully learned an $ε$-optimal policy with a sample complexity of $O(1/ε^2)$ trajectories with general function approximation when strategic exploration is necessary. We address this open problem by introducing a novel actor-critic algorithm that attains a sample-complexity of $O(dH^5 \log|\mathcal{A}|/ε^2 + d H^4 \log|\mathcal{F}|/ ε^2)$ trajectories, and accompanying $\sqrt{T}$ regret when the Bellman eluder dimension $d$ does not increase with $T$ at more than a $\log T$ rate. Here, $\mathcal{F}$ is the critic function class, $\mathcal{A}$ is the action space, and $H$ is the horizon in the finite horizon MDP setting. Our algorithm integrates optimism, off-policy critic estimation targeting the optimal Q-function, and rare-switching policy resets. We extend this to the setting of Hybrid RL, showing that initializing the critic with offline data yields sample efficiency gains compared to purely offline or online RL. Further, utilizing access to offline data, we provide a \textit{non-optimistic} provably efficient actor-critic algorithm that only additionally requires $N_{\text{off}} \geq c_{\text{off}}^*dH^4/ε^2$ in exchange for omitting optimism, where $c_{\text{off}}^*$ is the single-policy concentrability coefficient and $N_{\text{off}}$ is the number of offline samples. This addresses another open problem in the literature. We further provide numerical experiments to support our theoretical findings.

Sachin Garg, Kevin Tan, Michał Dereziński

Matrix sketching is a powerful tool for reducing the size of large data matrices. Yet there are fundamental limitations to this size reduction when we want to recover an accurate estimator for a task such as least square regression. We show that these limitations can be circumvented in the distributed setting by designing sketching methods that minimize the bias of the estimator, rather than its error. In particular, we give a sparse sketching method running in optimal space and current matrix multiplication time, which recovers a nearly-unbiased least squares estimator using two passes over the data. This leads to new communication-efficient distributed averaging algorithms for least squares and related tasks, which directly improve on several prior approaches. Our key novelty is a new bias analysis for sketched least squares, giving a sharp characterization of its dependence on the sketch sparsity. The techniques include new higher-moment restricted Bai-Silverstein inequalities, which are of independent interest to the non-asymptotic analysis of deterministic equivalents for random matrices that arise from sketching.

Haimo Fang, Kevin Tan, Jonathan Pipping et al.

Explainable boosting machines (EBMs) are popular "glass-box" models that learn a set of univariate functions using boosting trees. These achieve explainability through visualizations of each feature's effect. However, unlike linear model coefficients, uncertainty quantification for the learned univariate functions requires computationally intensive bootstrapping, making it hard to know which features truly matter. We provide an alternative using recent advances in statistical inference for gradient boosting, deriving methods for statistical inference as well as end-to-end theoretical guarantees. Using a moving average instead of a sum of trees (Boulevard regularization) allows the boosting process to converge to a feature-wise kernel ridge regression. This produces asymptotically normal predictions that achieve the minimax-optimal mean squared error for fitting Lipschitz GAMs with $p$ features at rate $O(pn^{-2/3})$, successfully avoiding the curse of dimensionality. We then construct prediction intervals for the response and confidence intervals for each learned univariate function with a runtime independent of the number of datapoints, enabling further explainability within EBMs.

Wei Fan, Kevin Tan, Yuting Wei

Adaptively collected data has become ubiquitous within modern practice. However, even seemingly benign adaptive sampling schemes can introduce severe biases, rendering traditional statistical inference tools inapplicable. This can be mitigated by a property called stability, which states that if the rate at which an algorithm takes actions converges to a deterministic limit, one can expect that certain parameters are asymptotically normal. Building on a recent line of work for the multi-armed bandit setting, we show that the linear upper confidence bound (LinUCB) algorithm for linear bandits satisfies this property. In doing so, we painstakingly characterize the behavior of the eigenvalues and eigenvectors of the random design feature covariance matrix in the setting where the action set is the unit ball, showing that it decomposes into a rank-one direction that locks onto the true parameter and an almost-isotropic bulk that grows at a predictable $\sqrt{T}$ rate. This allows us to establish a central limit theorem for the LinUCB algorithm, establishing asymptotic normality for the limiting distribution of the estimation error where the convergence occurs at a $T^{-1/4}$ rate. The resulting Wald-type confidence sets and hypothesis tests do not depend on the feature covariance matrix and are asymptotically tighter than existing nonasymptotic confidence sets. Numerical simulations corroborate our findings.

Haimo Fang, Kevin Tan, Giles Hooker

Gradient boosting is widely popular due to its flexibility and predictive accuracy. However, statistical inference and uncertainty quantification for gradient boosting remain challenging and under-explored. We propose a unified framework for statistical inference in gradient boosting regression. Our framework integrates dropout or parallel training with a recently proposed regularization procedure that allows for a central limit theorem (CLT) for boosting. With these enhancements, we surprisingly find that increasing the dropout rate and the number of trees grown in parallel at each iteration substantially enhances signal recovery and overall performance. Our resulting algorithms enjoy similar CLTs, which we use to construct built-in confidence intervals, prediction intervals, and rigorous hypothesis tests for assessing variable importance. Numerical experiments demonstrate that our algorithms perform well, interpolate between regularized boosting and random forests, and confirm the validity of their built-in statistical inference procedures.

Kevin Tan, Fan Yang, Yuhao Chen

Accurate dietary monitoring is essential for promoting healthier eating habits. A key area of research is how people interact and consume food using utensils and hands. By tracking their position and orientation, it is possible to estimate the volume of food being consumed, or monitor eating behaviours, highly useful insights into nutritional intake that can be more reliable than popular methods such as self-reporting. Hence, this paper implements a system that analyzes stationary video feed of people eating, using 6D pose estimation to track hand and spoon movements to capture spatial position and orientation. In doing so, we examine the performance of two state-of-the-art (SOTA) video object segmentation (VOS) models, both quantitatively and qualitatively, and identify main sources of error within the system.

Dongping Fang, Lian Duan, Xiaojing Yuan et al.

Accurate prediction of medical conditions with straight past clinical evidence is a long-sought topic in the medical management and health insurance field. Although great progress has been made with machine learning algorithms, the medical community is still skeptical about the model accuracy and interpretability. This paper presents an innovative hierarchical attention deep learning model to achieve better prediction and clear interpretability that can be easily understood by medical professionals. This paper developed an Interpretable Hierarchical Attention Network (IHAN). IHAN uses a hierarchical attention structure that matches naturally with the medical history data structure and reflects patients encounter (date of service) sequence. The model attention structure consists of 3 levels: (1) attention on the medical code types (diagnosis codes, procedure codes, lab test results, and prescription drugs), (2) attention on the sequential medical encounters within a type, (3) attention on the individual medical codes within an encounter and type. This model is applied to predict the occurrence of stage 3 chronic kidney disease (CKD), using three years medical history of Medicare Advantage (MA) members from an American nationwide health insurance company. The model takes members medical events, both claims and Electronic Medical Records (EMR) data, as input, makes a prediction of stage 3 CKD and calculates contribution from individual events to the predicted outcome.

Adrian K. Davison, Cliff Lansley, Choon Ching Ng et al.

Micro-facial expressions are regarded as an important human behavioural event that can highlight emotional deception. Spotting these movements is difficult for humans and machines, however research into using computer vision to detect subtle facial expressions is growing in popularity. This paper proposes an individualised baseline micro-movement detection method using 3D Histogram of Oriented Gradients (3D HOG) temporal difference method. We define a face template consisting of 26 regions based on the Facial Action Coding System (FACS). We extract the temporal features of each region using 3D HOG. Then, we use Chi-square distance to find subtle facial motion in the local regions. Finally, an automatic peak detector is used to detect micro-movements above the newly proposed adaptive baseline threshold. The performance is validated on two FACS coded datasets: SAMM and CASME II. This objective method focuses on the movement of the 26 face regions. When comparing with the ground truth, the best result was an AUC of 0.7512 and 0.7261 on SAMM and CASME II, respectively. The results show that 3D HOG outperformed for micro-movement detection, compared to state-of-the-art feature representations: Local Binary Patterns in Three Orthogonal Planes and Histograms of Oriented Optical Flow.