Interactive Intelligent Tutoring Systems (ITSs) enhance traditional ITSs by promoting effective learning through interactions and problem resolution in online education. Yet, proactive engagement, prioritizing resource optimization with planning and assessment capabilities, is often overlooked in current ITS designs. In this work, we investigate a new task, named Goal-oriented Intelligent Tutoring Systems (GITS), which aims to enable the student's mastery of a designated concept by strategically planning a customized sequence of exercises and assessment. To address the problem of goal-oriented policy learning in GITS, we propose a novel graph-based reinforcement learning framework, named Planning-Assessment-Interaction (PAI). Specifically, we first leverage cognitive structure information to improve state representation learning and action selection for planning the next action, which can be either to tutor an exercise or to assess the target concept. Further, we use a dynamically updated cognitive diagnosis model to simulate student responses to exercises and concepts. Three benchmark datasets across different subjects are constructed for enabling offline academic research on GITS. Experimental results demonstrate the effectiveness and efficiency of PAI and extensive analyses of various types of students are conducted to showcase the challenges in this task.

Can a physicist make only finite errors in the endless pursuit of the law of nature? This millennium-old question of inductive inference is a fundamental, yet mysterious problem in philosophy, lacking rigorous justifications. While classic online learning theory and inductive inference share a similar sequential decision-making spirit, the former's reliance on an adaptive adversary and worst-case error bounds limits its applicability to the latter. In this work, we introduce the concept of non-uniform online learning, which we argue aligns more closely with the principles of inductive reasoning. This setting assumes a predetermined ground-truth hypothesis and considers non-uniform, hypothesis-wise error bounds. In the realizable setting, we provide a complete characterization of learnability with finite error: a hypothesis class is non-uniform learnable if and only if it's a countable union of Littlestone classes, no matter the observations are adaptively chosen or iid sampled. Additionally, we propose a necessary condition for the weaker criterion of consistency which we conjecture to be tight. To further promote our theory, we extend our result to the more realistic agnostic setting, showing that any countable union of Littlestone classes can be learnt with regret $\tilde{O}(\sqrt{T})$. We hope this work could offer a new perspective of interpreting the power of induction from an online learning viewpoint.

We present new upper and lower bounds on the number of learner mistakes in the `transductive' online learning setting of Ben-David, Kushilevitz and Mansour (1997). This setting is similar to standard online learning, except that the adversary fixes a sequence of instances $x_1,\dots,x_n$ to be labeled at the start of the game, and this sequence is known to the learner. Qualitatively, we prove a trichotomy, stating that the minimal number of mistakes made by the learner as $n$ grows can take only one of precisely three possible values: $n$, $\Theta\left(\log (n)\right)$, or $\Theta(1)$. Furthermore, this behavior is determined by a combination of the VC dimension and the Littlestone dimension. Quantitatively, we show a variety of bounds relating the number of mistakes to well-known combinatorial dimensions. In particular, we improve the known lower bound on the constant in the $\Theta(1)$ case from $\Omega\left(\sqrt{\log(d)}\right)$ to $\Omega(\log(d))$ where $d$ is the Littlestone dimension. Finally, we extend our results to cover multiclass classification and the agnostic setting.

We study a variant of online multiclass classification where the learner predicts a single label but receives a \textit{set of labels} as feedback. In this model, the learner is penalized for not outputting a label contained in the revealed set. We show that unlike online multiclass learning with single-label feedback, deterministic and randomized online learnability are \textit{not equivalent} in the realizable setting under set-valued feedback. In addition, we show that deterministic and randomized realizable learnability are equivalent if the Helly number of the collection of sets that can be revealed as feedback is finite. In light of this separation, we give two new combinatorial dimensions, named the Set Littlestone and Measure Shattering dimension, whose finiteness characterizes deterministic and randomized realizable learnability respectively. Additionally, these dimensions lower- and upper bound the deterministic and randomized minimax regret in the realizable setting. Going beyond the realizable setting, we prove that the Measure shattering dimension continues to characterize learnability and quantify minimax regret in the agnostic setting. Finally, we use our results to establish bounds on the minimax regret for three practical learning settings: online multilabel ranking, online multilabel classification, and real-valued prediction with interval-valued response.

Recent empirical studies found that arrivals in many real queueing systems exhibit a clustering or self-exciting behavior; that is, an arrival may increase the possibility of new arrivals. In some cases, such clustering behavior is intrinsic to the underlying system. For example, in the stock market, it is a common practice to split a large order into small child orders to reduce transaction cost. As a consequence, one observed arriving order may be followed by a sequence of other child orders (Abergel and Jedidi, 2015). As a natural extension of the classic Poisson process, Hawkes process has been used to model arrivals with self-excitement such as order flow in stock market (Abergel and Jedidi, 2015), infected patients during pandemic (Bertozzi et al., 2020), and the internet traffic in social media (Zhao et al., 2015). To understand the impact of self-excitement in the arrival process on the long-run performance of service systems, Koops et al. (2018) and Daw and Pender (2018) provided analytic solutions to steady-state moments on the number of people in system for different infinite-server systems with Hawkes arrivals.

In this study, we investigate the combination of indicators, including performance, behavioral engagement, and emotional engagement, to identify students experiencing difficulties. We analyzed data from two primary sources: digital traces extracted from th e Learning Management System (LMS) and images captured by students' webcams. The digital traces provided insights into students' interactions with the educational content, while the images were utilized to analyze their emotional expressions during learnin g activities. By utilizing real data collected from students at a French engineering school, recorded during the 2022 2023 academic year, we observed a correlation between positive emotional states and improved academic outcomes. These preliminary findings support the notion that emotions play a crucial role in differentiating between high achieving and low achieving students.

Facilitating online learning in spiking neural networks (SNNs) is a key step in developing event-based models that can adapt to changing environments and learn from continuous data streams in real-time. Although forward-mode differentiation enables online learning, its computational requirements restrict scalability. This is typically addressed through approximations that limit learning in deep models. In this study, we propose Online Training with Postsynaptic Estimates (OTPE) for training feed-forward SNNs, which approximates Real-Time Recurrent Learning (RTRL) by incorporating temporal dynamics not captured by current approximations, such as Online Training Through Time (OTTT) and Online Spatio-Temporal Learning (OSTL). We show improved scaling for multi-layer networks using a novel approximation of temporal effects on the subsequent layer's activity. This approximation incurs minimal overhead in the time and space complexity compared to similar algorithms, and the calculation of temporal effects remains local to each layer. We characterize the learning performance of our proposed algorithms on multiple SNN model configurations for rate-based and time-based encoding. OTPE exhibits the highest directional alignment to exact gradients, calculated with backpropagation through time (BPTT), in deep networks and, on time-based encoding, outperforms other approximate methods. We also observe sizeable gains in average performance over similar algorithms in offline training of Spiking Heidelberg Digits with equivalent hyper-parameters (OTTT/OSTL - 70.5%; OTPE - 75.2%; BPTT - 78.1%).

Online learning holds the promise of enabling efficient long-term credit assignment in recurrent neural networks. However, current algorithms fall short of offline backpropagation by either not being scalable or failing to learn long-range dependencies. Here we present a high-performance online learning algorithm that merely doubles the memory and computational requirements of a single inference pass. We achieve this by leveraging independent recurrent modules in multi-layer networks, an architectural motif that has recently been shown to be particularly powerful. Experiments on synthetic memory problems and on the challenging long-range arena benchmark suite reveal that our algorithm performs competitively, establishing a new standard for what can be achieved through online learning. This ability to learn long-range dependencies offers a new perspective on learning in the brain and opens a promising avenue in neuromorphic computing.

Online learning quantum states with the logarithmic loss (LL-OLQS) is a quantum generalization of online portfolio selection, a classic open problem in the field of online learning for over three decades. The problem also emerges in designing randomized optimization algorithms for maximum-likelihood quantum state tomography. Recently, Jezequel et al. (arXiv:2209.13932) proposed the VB-FTRL algorithm, the first nearly regret-optimal algorithm for OPS with moderate computational complexity. In this note, we generalize VB-FTRL for LL-OLQS. Let $d$ denote the dimension and $T$ the number of rounds. The generalized algorithm achieves a regret rate of $O ( d^2 \log ( d + T ) )$ for LL-OLQS. Each iteration of the algorithm consists of solving a semidefinite program that can be implemented in polynomial time by, e.g., cutting-plane methods. For comparison, the best-known regret rate for LL-OLQS is currently $O ( d^2 \log T )$, achieved by the exponential weight method. However, there is no explicit implementation available for the exponential weight method for LL-OLQS. To facilitate the generalization, we introduce the notion of VB-convexity. VB-convexity is a sufficient condition for the logarithmic barrier associated with any function to be convex and is of independent interest.

Contextual bandits (Auer, 2002; Langford and Zhang, 2007) represent a classical sequential decisionmaking problem where an agent aims to maximize cumulative reward based on context information. At each round t, the agent observes a context and must choose one of K available actions based on both the current context and previous observations. Once the agent selects an action, she observes the associated reward, which is then used to refine future decision-making. Contextual bandits are typical examples of reinforcement learning problems where a balance between exploring new actions and exploiting previously acquired information is necessary to achieve optimal long-term rewards. It has numerous real-world applications including personalized recommendation systems (Li et al., 2010; Bouneffouf et al., 2012), healthcare (Yom-Tov et al., 2017; Liao et al., 2020), and online education (Liu et al., 2014; Shaikh et al., 2019). Despite the extensive existing literature on contextual bandits, in many real-world applications, the agent never observes the context exactly.