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Pedagogical planners can provide adaptive support to students in narrative-centered learning environments by dynamically scaffolding student learning and tailoring problem scenarios. Reinforcement learning (RL) is frequently used for pedagogical planning in narrative-centered learning environments. However, RL-based pedagogical planning raises significant challenges due to the scarcity of data for training RL policies. Most prior work has relied on limited-size datasets and offline RL techniques for policy learning. Unfortunately, offline RL techniques do not support on-demand exploration and evaluation, which can adversely impact the quality of induced policies. To address the limitation of data scarcity and offline RL, we propose INSIGHT, an online RL framework for training data-driven pedagogical policies that optimize student learning in narrative-centered learning environments. The INSIGHT framework consists of three components: a narrative-centered learning environment simulator, a simulated student agent, and an RL-based pedagogical planner agent, which uses a reward metric that is associated with effective student learning processes. The framework enables the generation of synthetic data for on-demand exploration and evaluation of RL-based pedagogical planning. We have implemented INSIGHT with OpenAI Gym for a narrative-centered learning environment testbed with rule-based simulated student agents and a deep Q-learning-based pedagogical planner. Our results show that online deep RL algorithms can induce near-optimal pedagogical policies in the INSIGHT framework, while offline deep RL algorithms only find suboptimal policies even with large amounts of data.

 

The Gilbert–Varshamov bound non-constructively establishes the existence of binary codes of distance 1/2−є/2 and rate Ω(є2). In a breakthrough result, Ta-Shma [STOC 2017] constructed the first explicit family of nearly optimal binary codes with distance 1/2−є/2 and rate Ω(є2+α), where α → 0 as є → 0. Moreover, the codes in Ta-Shma’s construction are є-balanced, where the distance between distinct codewords is not only bounded from below by 1/2−є/2, but also from above by 1/2+є/2. Polynomial time decoding algorithms for (a slight modification of) Ta-Shma’s codes appeared in [FOCS 2020], and were based on the Sum-of-Squares (SoS) semidefinite programming hierarchy. The running times for these algorithms were of the form NOα(1) for unique decoding, and NOє,α(1) for the setting of “gentle list decoding”, with large exponents of N even when α is a fixed constant. We derive new algorithms for both these tasks, running in time Õє(N). Our algorithms also apply to the general setting of decoding direct-sum codes. Our algorithms follow from new structural and algorithmic results for collections of k-tuples (ordered hypergraphs) possessing a “structured expansion” property, which we call splittability. This property was previously identified and used in the analysis of SoS-based decoding and constraint satisfaction algorithms, and is also known to be satisfied by Ta-Shma’s code construction. We obtain a new weak regularity decomposition for (possibly sparse) splittable collections W ⊆ [n]k, similar to the regularity decomposition for dense structures by Frieze and Kannan [FOCS 1996]. These decompositions are also computable in near-linear time Õ(|W |), and form a key component of our algorithmic results. 

The Gilbert-Varshamov bound (non-constructively) establishes the existence of binary codes of distance 1/2-ε and rate Ω(ε 2 ) (where an upper bound of O(ε 2 log(1/ε)) is known). Ta-Shma [STOC 2017] gave an explicit construction of ε-balanced binary codes, where any two distinct codewords are at a distance between 1/2-ε/2 and 1/2+ε/2, achieving a near optimal rate of Ω(ε 2+β ), where β→ 0 as ε→ 0. We develop unique and list decoding algorithms for (a slight modification of) the family of codes constructed by Ta-Shma, in the adversarial error model. We prove the following results for ε-balanced codes with block length N and rate Ω(ε 2+β ) in this family: -For all , there are explicit codes which can be uniquely decoded up to an error of half the minimum distance in time N Oε,β(1) . -For any fixed constant β independent of ε, there is an explicit construction of codes which can be uniquely decoded up to an error of half the minimum distance in time (log(1/ε)) O(1) ·N Oβ(1) . -For any , there are explicit ε-balanced codes with rate Ω(ε 2+β ) which can be list decoded up to error 1/2-ε ' in time N Oε,ε' ,β(1), where ε ' ,β→ 0 as ε→ 0. The starting point of our algorithms is the framework for list decoding direct-sum codes develop in Alev et al. [SODA 2020], which uses the Sum-of-Squares SDP hierarchy. The rates obtained there were quasipolynomial in ε. Here, we show how to overcome the far from optimal rates of this framework obtaining unique decoding algorithms for explicit binary codes of near optimal rate. These codes are based on simple modifications of Ta-Shma's construction.