Bo Dai
My research interests lie on designing principled machine learning methods. Currently, I mainly focus on three major themes:
- Reinforcement learning: design effective algorithms by exploiting the intrinsic structures in the uncertain dynamics for automatic decision making.
- Learning to design algorithms: improve the algorithms, e.g., sampling, searching and planning, by leveraging empirical experiences.
- Structured input and output: build effective models for capturing the structures information in input and output, e.g., binaries, sequences, programs, trees, and graphs.
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Stochastic dual dynamic programming~(SDDP) is one of the state-of-the-art algorithm for multi-stage stochastic optimization, yet its cost exponentially increases w.r.t. the size of decision variables, therefore, quickly becomes inapplicable for high-dimension problems. We introduce a neuralized component into SDDP, which outputs a \emph{piece-wise linear function} in a \emph{low-dimension} space to approximate the value function, based on the \emph{context of the problem instances}. The neuralized component will consistently evolve to abstract effective low-dimension action space and improve the quality of value function approximation for each problem based on prior successful experiences. It is seamlessly integrated with SDDP, formed our neural enhanced solver,~\AlgName~(\algshort), which achieves the optimality \emph{without loss of accuracy} in \emph{faster speed} for high-dimension and long-horizon multi-stage stochastic optimizations. We conduct thorough empirical experiments to demonstrate the benefits of \algshort from transferability on scalability.~\algshort significantly outperforms the competitors, including SDDP and variants of RL algorithms, in terms of solution quality and feasibility, and computational speed.
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A goal for multi-task learning from a multi-objective optimization perspective is to find the Pareto solutions that are not dominated by others. In this paper, we provide some insights on understanding the trade-off between Pareto efficiency and generalization, as a result of parameterization in deep learning: as a multi-objective optimization problem, enough parameterization is needed for handling task conflicts in a constrained solution space; however, from a multi-task generalization perspective, over-parameterization undermines the benefit of learning a shared representation which helps harder tasks or tasks with limited training examples. A delicate balance between multi-task generalization and multi-objective optimization is therefore needed for finding a better trade-off between efficiency and generalization. To this end, we propose a method of under-parameterized self-auxiliaries for multi-task models to achieve the best of both worlds. It is model-agnostic, task-agnostic and works with other multi-task learning algorithms. Empirical results show our method improves Pareto efficiency over existing popular algorithms on several multi-task applications.
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Score-based modeling through stochastic differential equations (SDEs) has provided a new perspective on diffusion models, and demonstrated superior performance on continuous data. However, the gradient of the log-likelihood function, i.e., the score function, is not properly defined for discrete spaces. This makes it non-trivial to adapt the score-based modeling to categorical data. In this paper, we extend diffusion models to discrete variables by introducing a stochastic jump process where the reverse process denoises via a continuous-time Markov chain. This formulation admits an analytical simulation during backward sampling. To learn the reverse process, we extend score matching to general categorical data, and show that an unbiased estimator can be obtained via simple matching of the conditional marginal distributions. We demonstrate the effectiveness of the proposed method on a set of synthetic and real-world music and image benchmarks.
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We study stochastic policy optimization in the on-policy case and make the following four contributions. \textit{First}, we show that the ordering of optimization algorithms by their efficiency gets reversed when they have or they not to the true gradient information. In particular, this finding implies that, unlike in the true gradient scenario, geometric information cannot be easily exploited without detrimental consequences in stochastic policy optimization. \textit{Second}, to explain these findings we introduce the concept of \textit{committal rate} for stochastic policy optimization, and show that this can serve as a criterion for determining almost sure convergence to global optimality. \textit{Third}, we show that if there is no external mechanism that allows an algorithm to determine the difference between optimal and sub-optimal actions using only on-policy samples, then there must be an inherent trade-off between exploiting geometry to accelerate convergence versus achieving optimality almost surely. That is, an algorithm either converges to a globally optimal policy with probability $1$ but at a rate no better than $O(1/t)$, or it achieves a faster than $O(1/t)$ convergence rate but then must fail to converge to the globally optimal deterministic policy with some positive probability. \textit{Finally}, we use our committal rate theory to explain why practical policy optimization methods are sensitive to random initialization, and how an ensemble method with parallelism can be guaranteed to achieve near-optimal solutions with high probability.
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On the Optimality of Batch Policy Optimization Algorithms
Chenjun Xiao
Yifan Wu
Tor Lattimore
Jincheng Mei
Lihong Li
ICML 2021(2021)
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Batch policy optimization considers leveraging existing data for policy construction before interacting with an environment. Although interest in this problem has grown significantly in recent years, its theoretical foundations remain under-developed. To advance the understanding of this problem, we provide three results that characterize the limits and possibilities of batch policy optimization in the finite-armed stochastic bandit setting. First, we introduce a class of confidence-adjusted index algorithms that unifies optimistic and pessimistic principles in a common framework, which enables a general analysis. For this family, we show that any confidence-adjusted index algorithm is minimax optimal, whether it be optimistic, pessimistic or neutral. Our analysis reveals that instance-dependent optimality, commonly used to establish optimality of on-line stochastic bandit algorithms, cannot be achieved by any algorithm in the batch setting. In particular, for any algorithm that performs optimally in some environment, there exists another environment where the same algorithm suffers arbitrarily larger regret. Therefore, to establish a framework for distinguishing algorithms, we introduce a new weighted-minimax criterion that considers the inherent difficulty of optimal value prediction. We demonstrate how this criterion can be used to justify commonly used pessimistic principles for batch policy optimization.
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Classical global convergence results for first-order methods rely on uniform smoothness and the Łojasiewicz inequality. Motivated by properties of objective functions that arise in machine learning, we propose a non-uniform refinement of these notions, leading to \emph{Non-uniform Smoothness} (NS) and \emph{Non-uniform Łojasiewicz inequality} (NŁ). The new definitions inspire new geometry-aware first-order methods that are able to converge to global optimality faster than the classical Ω(1/t2) lower bounds. To illustrate the power of these geometry-aware methods and their corresponding non-uniform analysis, we consider two important problems in machine learning: policy gradient optimization in reinforcement learning (PG), and generalized linear model training in supervised learning (GLM). For PG, we find that normalizing the gradient ascent method can accelerate convergence to O(e−t) while incurring less overhead than existing algorithms. For GLM, we show that geometry-aware normalized gradient descent can also achieve a linear convergence rate, which significantly improves the best known results. We additionally show that the proposed geometry-aware descent methods escape landscape plateaus faster than standard gradient descent. Experimental results are used to illustrate and complement the theoretical findings.
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Reliable automatic evaluation of dialogue systems under an interactive environment has long been overdue. An ideal environment for evaluating dialog systems, also known as the Turing test, needs to involve human interaction, which is usually not affordable for large-scale experiments. Though researchers have attempted to use metrics (e.g., perplexity, BLEU) in language generation tasks or some model-based reinforcement learning methods (e.g., self-play evaluation) for automatic evaluation, these methods only show a very weak correlation with the actual human evaluation in practice. To bridge such a gap, we propose a new framework named ENIGMA for estimating human evaluation scores based on recent advances of off-policy evaluation in reinforcement learning. ENIGMA only requires a handful of pre-collected experience data, and therefore does not involve human interaction with the target policy during the evaluation, making automatic evaluations feasible. More importantly, ENIGMA is model-free and agnostic to the behavior policies for collecting the experience data (see details in Section 2), which significantly alleviates the technical difficulties of modeling complex dialogue environments and human behaviors. Our experiments show that ENIGMA significantly outperforms existing methods in terms of correlation with human evaluation scores.
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Retrosynthesis is the process of identifying a set of reactants to synthesize a target molecule. It is critical to material design and drug discovery. Existing machine learning approaches based on language models and graph neural networks have achieved encouraging results. However, the inner connections of these models are rarely discussed, and rigorous evaluations of these models are largely in need. In this paper, we propose a framework that unifies sequence- and graph-based methods as energy-based models (EBMs) with different energy functions. This unified view establishes connections and reveals the differences between models, thereby enhances our understanding of model design. We also provide a comprehensive assessment of performance to the community. Additionally, we present a novel dual variant within the framework that performs consistent training to induce the agreement between forward- and backward-prediction. This model improves the state-of-the-art of template-free methods with or without reaction types.
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LEGO: Latent Execution-Guided Reasoning for Multi-Hop Question Answering on Knowledge Graphs
Hongyu Ren
Michihiro Yasunaga
Haitian Sun
Jure Leskovec
ICML 2021
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Answering complex natural language questions on knowledge graphs (KGQA) is a challenging task. It requires reasoning with the input natural language questions as well as a massive, incomplete heterogeneous KG. Prior methods obtain an abstract structured query graph/tree from the input question and traverse the KG for answers following the query tree. However, they inherently cannot deal with missing links in the KG. Here we present LEGO, a Latent Execution-Guided reasOning framework to handle this challenge in KGQA. LEGO works in an iterative way, which alternates between (1) a Query Synthesizer, which synthesizes a reasoning action and grows the query tree step-by-step, and (2) a Latent Space Executor that executes the reasoning action in the latent embedding space to combat against the missing information in KG. To learn the synthesizer without step-wise supervision, we design a generic latent execution guided bottom-up search procedure to find good execution traces efficiently in the vast query space. Experimental results on several KGQA benchmarks demonstrate the effectiveness of our framework compared with previous state of the art.
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Adversarial training provides a principled approach for training robust neural networks. From an optimization perspective, adversarial training is essentially solving a bilevel optimization problem. The leader problem is trying to learn a robust classifier, while the follower problem is trying to generate adversarial samples. Unfortunately, such a bilevel problem is difficult to solve due to its highly complicated structure. This work proposes a new adversarial training method based on a generic learning-to-learn (L2L) framework. Specifically, instead of applying existing hand-designed algorithms for the inner problem, we learn an optimizer, which is parametrized as a convolutional neural network. At the same time, a robust classifier is learned to defense the adversarial attack generated by the learned optimizer. Experiments over CIFAR-10 and CIFAR-100 datasets demonstrate that L2L outperforms existing adversarial training methods in both classification accuracy and computational efficiency. Moreover, our L2L framework can be extended to generative adversarial imitation learning and stabilize the training.
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