Falcon Z. Dai

Falcon Z. Dai

A Markov decision process can be parameterized by a transition kernel and a reward function. Both play essential roles in the study of reinforcement learning as evidenced by their presence in the Bellman equations. In our inquiry of various kinds of "costs" associated with reinforcement learning inspired by the demands in robotic applications, rewards are central to understanding the structure of a Markov decision process and reward-centric notions can elucidate important concepts in reinforcement learning. Specifically, we study the sample complexity of policy evaluation and develop a novel estimator with an instance-specific error bound of $\tilde{O}(\sqrt{\frac{τ_s}{n}})$ for estimating a single state value. Under the online regret minimization setting, we refine the transition-based MDP constant, diameter, into a reward-based constant, maximum expected hitting cost, and with it, provide a theoretical explanation for how a well-known technique, potential-based reward shaping, could accelerate learning with expert knowledge. In an attempt to study safe reinforcement learning, we model hazardous environments with irrecoverability and proposed a quantitative notion of safe learning via reset efficiency. In this setting, we modify a classic algorithm to account for resets achieving promising preliminary numerical results. Lastly, for MDPs with multiple reward functions, we develop a planning algorithm that computationally efficiently finds Pareto-optimal stochastic policies.

Falcon Z. Dai

Being inspired by the success of \texttt{word2vec} \citep{mikolov2013distributed} in capturing analogies, we study the conjecture that analogical relations can be represented by vector spaces. Unlike many previous works that focus on the distributional semantic aspect of \texttt{word2vec}, we study the purely \emph{representational} question: can \emph{all} semantic word-word relations be represented by differences (or directions) of vectors? We call this the word2vec conjecture and point out some of its desirable implications. However, we will exhibit a class of relations that cannot be represented in this way, thus falsifying the conjecture and establishing a limitative result for the representability of semantic relations by vector spaces over fields of characteristic 0, e.g., real or complex numbers.

Falcon Z. Dai, Matthew R. Walter

At the working heart of policy iteration algorithms commonly used and studied in the discounted setting of reinforcement learning, the policy evaluation step estimates the value of states with samples from a Markov reward process induced by following a Markov policy in a Markov decision process. We propose a simple and efficient estimator called loop estimator that exploits the regenerative structure of Markov reward processes without explicitly estimating a full model. Our method enjoys a space complexity of $O(1)$ when estimating the value of a single positive recurrent state $s$ unlike TD with $O(S)$ or model-based methods with $O\left(S^2\right)$. Moreover, the regenerative structure enables us to show, without relying on the generative model approach, that the estimator has an instance-dependent convergence rate of $\widetilde{O}\left(\sqrt{τ_s/T}\right)$ over steps $T$ on a single sample path, where $τ_s$ is the maximal expected hitting time to state $s$. In preliminary numerical experiments, the loop estimator outperforms model-free methods, such as TD(k), and is competitive with the model-based estimator.

Igor Vasiljevic, Nick Kolkin, Shanyi Zhang et al.

We introduce DIODE, a dataset that contains thousands of diverse high resolution color images with accurate, dense, long-range depth measurements. DIODE (Dense Indoor/Outdoor DEpth) is the first public dataset to include RGBD images of indoor and outdoor scenes obtained with one sensor suite. This is in contrast to existing datasets that focus on just one domain/scene type and employ different sensors, making generalization across domains difficult. The dataset is available for download at http://diode-dataset.org

Falcon Z. Dai, Zheng Cai

We show that the imperceptibility of several existing linguistic steganographic systems (Fang et al., 2017; Yang et al., 2018) relies on implicit assumptions on statistical behaviors of fluent text. We formally analyze them and empirically evaluate these assumptions. Furthermore, based on these observations, we propose an encoding algorithm called patient-Huffman with improved near-imperceptible guarantees.

Falcon Z. Dai, Matthew R. Walter

We propose a new complexity measure for Markov decision processes (MDPs), the maximum expected hitting cost (MEHC). This measure tightens the closely related notion of diameter [JOA10] by accounting for the reward structure. We show that this parameter replaces diameter in the upper bound on the optimal value span of an extended MDP, thus refining the associated upper bounds on the regret of several UCRL2-like algorithms. Furthermore, we show that potential-based reward shaping [NHR99] can induce equivalent reward functions with varying informativeness, as measured by MEHC. We further establish that shaping can reduce or increase MEHC by at most a factor of two in a large class of MDPs with finite MEHC and unsaturated optimal average rewards.

Sebastian Gehrmann, Falcon Z. Dai, Henry Elder et al.

Learning to generate fluent natural language from structured data with neural networks has become an common approach for NLG. This problem can be challenging when the form of the structured data varies between examples. This paper presents a survey of several extensions to sequence-to-sequence models to account for the latent content selection process, particularly variants of copy attention and coverage decoding. We further propose a training method based on diverse ensembling to encourage models to learn distinct sentence templates during training. An empirical evaluation of these techniques shows an increase in the quality of generated text across five automated metrics, as well as human evaluation.

Falcon Z. Dai, Zheng Cai

Given the advantage and recent success of English character-level and subword-unit models in several NLP tasks, we consider the equivalent modeling problem for Chinese. Chinese script is logographic and many Chinese logograms are composed of common substructures that provide semantic, phonetic and syntactic hints. In this work, we propose to explicitly incorporate the visual appearance of a character's glyph in its representation, resulting in a novel glyph-aware embedding of Chinese characters. Being inspired by the success of convolutional neural networks in computer vision, we use them to incorporate the spatio-structural patterns of Chinese glyphs as rendered in raw pixels. In the context of two basic Chinese NLP tasks of language modeling and word segmentation, the model learns to represent each character's task-relevant semantic and syntactic information in the character-level embedding.