arXiv subjects

Botao Hao

Publications and source records attributed to Botao Hao.

At least 19 recordsLinked to original sources

arXiv2026

Learning What to Recommend: Minimax Optimal Simple Regret in Logistic Bandits

We study stochastic logistic bandits with $d$-dimensional action features under the simple-regret objective, where a learner uses $T$ rounds of exploration to output a single final action. The logistic structure is essential here: because the informativeness of an action depends on the local curvature of the sigmoid, actions that are best for immediate reward need not be the most useful for identifying the best final recommendation. We show that the first-order minimax difficulty is governed by $κ_*$, the inverse slope of the sigmoid at the optimal action. The lower bound is realized by a shifted saturated hard family in which saturation simultaneously limits the information available about the final decision and controls the value loss from a wrong recommendation. This reveals a hard mechanism distinct from cumulative-regret constructions, even though online-to-batch reductions recover the same leading order in expectation. We then develop two curvature-aware algorithms: \MULog, a pure-exploration method whose final recommendation satisfies a high-probability upper bound of order $\tilde O(d/\sqrt{κ_* T})$, matching the lower bound up to logarithmic factors, and \THATS, a Thompson-sampling-style method that provides a computationally lighter alternative. Experiments on both hard and easy geometries support the same picture: informative low-reward actions can make instances substantially easier, and the curvature-aware methods exploit this structure especially effectively.

cs.LG↗

arXiv2026

OpenAI GPT-5 System Card

This is the system card published alongside the OpenAI GPT-5 launch, August 2025. GPT-5 is a unified system with a smart and fast model that answers most questions, a deeper reasoning model for harder problems, and a real-time router that quickly decides which model to use based on conversation type, complexity, tool needs, and explicit intent (for example, if you say 'think hard about this' in the prompt). The router is continuously trained on real signals, including when users switch models, preference rates for responses, and measured correctness, improving over time. Once usage limits are reached, a mini version of each model handles remaining queries. This system card focuses primarily on gpt-5-thinking and gpt-5-main, while evaluations for other models are available in the appendix. The GPT-5 system not only outperforms previous models on benchmarks and answers questions more quickly, but -- more importantly -- is more useful for real-world queries. We've made significant advances in reducing hallucinations, improving instruction following, and minimizing sycophancy, and have leveled up GPT-5's performance in three of ChatGPT's most common uses: writing, coding, and health. All of the GPT-5 models additionally feature safe-completions, our latest approach to safety training to prevent disallowed content. Similarly to ChatGPT agent, we have decided to treat gpt-5-thinking as High capability in the Biological and Chemical domain under our Preparedness Framework, activating the associated safeguards. While we do not have definitive evidence that this model could meaningfully help a novice to create severe biological harm -- our defined threshold for High capability -- we have chosen to take a precautionary approach.

cs.CL↗

arXiv2026

OpenAI o1 System Card

The o1 model series is trained with large-scale reinforcement learning to reason using chain of thought. These advanced reasoning capabilities provide new avenues for improving the safety and robustness of our models. In particular, our models can reason about our safety policies in context when responding to potentially unsafe prompts, through deliberative alignment. This leads to state-of-the-art performance on certain benchmarks for risks such as generating illicit advice, choosing stereotyped responses, and succumbing to known jailbreaks. Training models to incorporate a chain of thought before answering has the potential to unlock substantial benefits, while also increasing potential risks that stem from heightened intelligence. Our results underscore the need for building robust alignment methods, extensively stress-testing their efficacy, and maintaining meticulous risk management protocols. This report outlines the safety work carried out for the OpenAI o1 and OpenAI o1-mini models, including safety evaluations, external red teaming, and Preparedness Framework evaluations.

cs.AI↗

arXiv2024

Efficient Exploration for LLMs

We present evidence of substantial benefit from efficient exploration in gathering human feedback to improve large language models. In our experiments, an agent sequentially generates queries while fitting a reward model to the feedback received. Our best-performing agent generates queries using double Thompson sampling, with uncertainty represented by an epistemic neural network. Our results demonstrate that efficient exploration enables high levels of performance with far fewer queries. Further, both uncertainty estimation and the choice of exploration scheme play critical roles.

cs.LG↗

arXiv2024

Stochastic Low-rank Tensor Bandits for Multi-dimensional Online Decision Making

Multi-dimensional online decision making plays a crucial role in many real applications such as online recommendation and digital marketing. In these problems, a decision at each time is a combination of choices from different types of entities. To solve it, we introduce stochastic low-rank tensor bandits, a class of bandits whose mean rewards can be represented as a low-rank tensor. We consider two settings, tensor bandits without context and tensor bandits with context. In the first setting, the platform aims to find the optimal decision with the highest expected reward, a.k.a, the largest entry of true reward tensor. In the second setting, some modes of the tensor are contexts and the rest modes are decisions, and the goal is to find the optimal decision given the contextual information. We propose two learning algorithms tensor elimination and tensor epoch-greedy for tensor bandits without context, and derive finite-time regret bounds for them. Comparing with existing competitive methods, tensor elimination has the best overall regret bound and tensor epoch-greedy has a sharper dependency on dimensions of the reward tensor. Furthermore, we develop a practically effective Bayesian algorithm called tensor ensemble sampling for tensor bandits with context. Extensive simulations and real analysis in online advertising data back up our theoretical findings and show that our algorithms outperform various state-of-the-art approaches that ignore the tensor low-rank structure.

stat.ML↗

arXiv2024

Efficient Online Learning with Offline Datasets for Infinite Horizon MDPs: A Bayesian Approach

In this paper, we study the problem of efficient online reinforcement learning in the infinite horizon setting when there is an offline dataset to start with. We assume that the offline dataset is generated by an expert but with unknown level of competence, i.e., it is not perfect and not necessarily using the optimal policy. We show that if the learning agent models the behavioral policy (parameterized by a competence parameter) used by the expert, it can do substantially better in terms of minimizing cumulative regret, than if it doesn't do that. We establish an upper bound on regret of the exact informed PSRL algorithm that scales as $\tilde{O}(\sqrt{T})$. This requires a novel prior-dependent regret analysis of Bayesian online learning algorithms for the infinite horizon setting. We then propose the Informed RLSVI algorithm to efficiently approximate the iPSRL algorithm.

cs.LG↗

arXiv2023

Bridging Imitation and Online Reinforcement Learning: An Optimistic Tale

In this paper, we address the following problem: Given an offline demonstration dataset from an imperfect expert, what is the best way to leverage it to bootstrap online learning performance in MDPs. We first propose an Informed Posterior Sampling-based RL (iPSRL) algorithm that uses the offline dataset, and information about the expert's behavioral policy used to generate the offline dataset. Its cumulative Bayesian regret goes down to zero exponentially fast in N, the offline dataset size if the expert is competent enough. Since this algorithm is computationally impractical, we then propose the iRLSVI algorithm that can be seen as a combination of the RLSVI algorithm for online RL, and imitation learning. Our empirical results show that the proposed iRLSVI algorithm is able to achieve significant reduction in regret as compared to two baselines: no offline data, and offline dataset but used without information about the generative policy. Our algorithm bridges online RL and imitation learning for the first time.

cs.LG↗

arXiv2023

Sample Efficient Deep Reinforcement Learning via Local Planning

The focus of this work is sample-efficient deep reinforcement learning (RL) with a simulator. One useful property of simulators is that it is typically easy to reset the environment to a previously observed state. We propose an algorithmic framework, named uncertainty-first local planning (UFLP), that takes advantage of this property. Concretely, in each data collection iteration, with some probability, our meta-algorithm resets the environment to an observed state which has high uncertainty, instead of sampling according to the initial-state distribution. The agent-environment interaction then proceeds as in the standard online RL setting. We demonstrate that this simple procedure can dramatically improve the sample cost of several baseline RL algorithms on difficult exploration tasks. Notably, with our framework, we can achieve super-human performance on the notoriously hard Atari game, Montezuma's Revenge, with a simple (distributional) double DQN. Our work can be seen as an efficient approximate implementation of an existing algorithm with theoretical guarantees, which offers an interpretation of the positive empirical results.

cs.LG↗

arXiv2023

Leveraging Demonstrations to Improve Online Learning: Quality Matters

We investigate the extent to which offline demonstration data can improve online learning. It is natural to expect some improvement, but the question is how, and by how much? We show that the degree of improvement must depend on the quality of the demonstration data. To generate portable insights, we focus on Thompson sampling (TS) applied to a multi-armed bandit as a prototypical online learning algorithm and model. The demonstration data is generated by an expert with a given competence level, a notion we introduce. We propose an informed TS algorithm that utilizes the demonstration data in a coherent way through Bayes' rule and derive a prior-dependent Bayesian regret bound. This offers insight into how pretraining can greatly improve online performance and how the degree of improvement increases with the expert's competence level. We also develop a practical, approximate informed TS algorithm through Bayesian bootstrapping and show substantial empirical regret reduction through experiments.

cs.LG↗

arXiv2023

Sequential Best-Arm Identification with Application to Brain-Computer Interface

A brain-computer interface (BCI) is a technology that enables direct communication between the brain and an external device or computer system. It allows individuals to interact with the device using only their thoughts, and holds immense potential for a wide range of applications in medicine, rehabilitation, and human augmentation. An electroencephalogram (EEG) and event-related potential (ERP)-based speller system is a type of BCI that allows users to spell words without using a physical keyboard, but instead by recording and interpreting brain signals under different stimulus presentation paradigms. Conventional non-adaptive paradigms treat each word selection independently, leading to a lengthy learning process. To improve the sampling efficiency, we cast the problem as a sequence of best-arm identification tasks in multi-armed bandits. Leveraging pre-trained large language models (LLMs), we utilize the prior knowledge learned from previous tasks to inform and facilitate subsequent tasks. To do so in a coherent way, we propose a sequential top-two Thompson sampling (STTS) algorithm under the fixed-confidence setting and the fixed-budget setting. We study the theoretical property of the proposed algorithm, and demonstrate its substantial empirical improvement through both synthetic data analysis as well as a P300 BCI speller simulator example.

cs.HC↗

arXiv2022

Regret Bounds for Information-Directed Reinforcement Learning

Information-directed sampling (IDS) has revealed its potential as a data-efficient algorithm for reinforcement learning (RL). However, theoretical understanding of IDS for Markov Decision Processes (MDPs) is still limited. We develop novel information-theoretic tools to bound the information ratio and cumulative information gain about the learning target. Our theoretical results shed light on the importance of choosing the learning target such that the practitioners can balance the computation and regret bounds. As a consequence, we derive prior-free Bayesian regret bounds for vanilla-IDS which learns the whole environment under tabular finite-horizon MDPs. In addition, we propose a computationally-efficient regularized-IDS that maximizes an additive form rather than the ratio form and show that it enjoys the same regret bound as vanilla-IDS. With the aid of rate-distortion theory, we improve the regret bound by learning a surrogate, less informative environment. Furthermore, we extend our analysis to linear MDPs and prove similar regret bounds for Thompson sampling as a by-product.

cs.LG↗

arXiv2022

The Neural Testbed: Evaluating Joint Predictions

Predictive distributions quantify uncertainties ignored by point estimates. This paper introduces The Neural Testbed: an open-source benchmark for controlled and principled evaluation of agents that generate such predictions. Crucially, the testbed assesses agents not only on the quality of their marginal predictions per input, but also on their joint predictions across many inputs. We evaluate a range of agents using a simple neural network data generating process. Our results indicate that some popular Bayesian deep learning agents do not fare well with joint predictions, even when they can produce accurate marginal predictions. We also show that the quality of joint predictions drives performance in downstream decision tasks. We find these results are robust across choice a wide range of generative models, and highlight the practical importance of joint predictions to the community.

cs.LG↗

arXiv2022

Contextual Information-Directed Sampling

Information-directed sampling (IDS) has recently demonstrated its potential as a data-efficient reinforcement learning algorithm. However, it is still unclear what is the right form of information ratio to optimize when contextual information is available. We investigate the IDS design through two contextual bandit problems: contextual bandits with graph feedback and sparse linear contextual bandits. We provably demonstrate the advantage of contextual IDS over conditional IDS and emphasize the importance of considering the context distribution. The main message is that an intelligent agent should invest more on the actions that are beneficial for the future unseen contexts while the conditional IDS can be myopic. We further propose a computationally-efficient version of contextual IDS based on Actor-Critic and evaluate it empirically on a neural network contextual bandit.

cs.LG↗

arXiv2022

Bootstrapping Fitted Q-Evaluation for Off-Policy Inference

Bootstrapping provides a flexible and effective approach for assessing the quality of batch reinforcement learning, yet its theoretical property is less understood. In this paper, we study the use of bootstrapping in off-policy evaluation (OPE), and in particular, we focus on the fitted Q-evaluation (FQE) that is known to be minimax-optimal in the tabular and linear-model cases. We propose a bootstrapping FQE method for inferring the distribution of the policy evaluation error and show that this method is asymptotically efficient and distributionally consistent for off-policy statistical inference. To overcome the computation limit of bootstrapping, we further adapt a subsampling procedure that improves the runtime by an order of magnitude. We numerically evaluate the bootrapping method in classical RL environments for confidence interval estimation, estimating the variance of off-policy evaluator, and estimating the correlation between multiple off-policy evaluators.

stat.ML↗

arXiv2022

Interacting Contour Stochastic Gradient Langevin Dynamics

We propose an interacting contour stochastic gradient Langevin dynamics (ICSGLD) sampler, an embarrassingly parallel multiple-chain contour stochastic gradient Langevin dynamics (CSGLD) sampler with efficient interactions. We show that ICSGLD can be theoretically more efficient than a single-chain CSGLD with an equivalent computational budget. We also present a novel random-field function, which facilitates the estimation of self-adapting parameters in big data and obtains free mode explorations. Empirically, we compare the proposed algorithm with popular benchmark methods for posterior sampling. The numerical results show a great potential of ICSGLD for large-scale uncertainty estimation tasks.

stat.ML↗

arXiv2022

Efficient Local Planning with Linear Function Approximation

We study query and computationally efficient planning algorithms with linear function approximation and a simulator. We assume that the agent only has local access to the simulator, meaning that the agent can only query the simulator at states that have been visited before. This setting is more practical than many prior works on reinforcement learning with a generative model. We propose two algorithms, named confident Monte Carlo least square policy iteration (Confident MC-LSPI) and confident Monte Carlo Politex (Confident MC-Politex) for this setting. Under the assumption that the Q-functions of all policies are linear in known features of the state-action pairs, we show that our algorithms have polynomial query and computational costs in the dimension of the features, the effective planning horizon, and the targeted sub-optimality, while these costs are independent of the size of the state space. One technical contribution of our work is the introduction of a novel proof technique that makes use of a virtual policy iteration algorithm. We use this method to leverage existing results on $\ell_\infty$-bounded approximate policy iteration to show that our algorithm can learn the optimal policy for the given initial state even only with local access to the simulator. We believe that this technique can be extended to broader settings beyond this work.

cs.LG↗

arXiv2021

High-Dimensional Sparse Linear Bandits

Stochastic linear bandits with high-dimensional sparse features are a practical model for a variety of domains, including personalized medicine and online advertising. We derive a novel $Ω(n^{2/3})$ dimension-free minimax regret lower bound for sparse linear bandits in the data-poor regime where the horizon is smaller than the ambient dimension and where the feature vectors admit a well-conditioned exploration distribution. This is complemented by a nearly matching upper bound for an explore-then-commit algorithm showing that that $Θ(n^{2/3})$ is the optimal rate in the data-poor regime. The results complement existing bounds for the data-rich regime and provide another example where carefully balancing the trade-off between information and regret is necessary. Finally, we prove a dimension-free $O(\sqrt{n})$ regret upper bound under an additional assumption on the magnitude of the signal for relevant features.

stat.ML↗

arXiv2021

Bandit Phase Retrieval

We study a bandit version of phase retrieval where the learner chooses actions $(A_t)_{t=1}^n$ in the $d$-dimensional unit ball and the expected reward is $\langle A_t, θ_\star\rangle^2$ where $θ_\star \in \mathbb R^d$ is an unknown parameter vector. We prove that the minimax cumulative regret in this problem is $\smash{\tilde Θ(d \sqrt{n})}$, which improves on the best known bounds by a factor of $\smash{\sqrt{d}}$. We also show that the minimax simple regret is $\smash{\tilde Θ(d / \sqrt{n})}$ and that this is only achievable by an adaptive algorithm. Our analysis shows that an apparently convincing heuristic for guessing lower bounds can be misleading and that uniform bounds on the information ratio for information-directed sampling are not sufficient for optimal regret.

stat.ML↗