Autonomous agents optimize the reward function we give them. What they don't know is how hard it is for us to design a reward function that actually captures what we want. When designing the reward, we might think of some specific training scenarios, and make sure that the reward will lead to the right behavior in those scenarios. Inevitably, agents encounter new scenarios (e.g., new types of terrain) where optimizing that same reward may lead to undesired behavior. Our insight is that reward functions are merely observations about what the designer actually wants, and that they should be interpreted in the context in which they were designed. We introduce inverse reward design (IRD) as the problem of inferring the true objective based on the designed reward and the training MDP. We introduce approximate methods for solving IRD problems, and use their solution to plan risk-averse behavior in test MDPs. Empirical results suggest that this approach can help alleviate negative side effects of misspecified reward functions and mitigate reward hacking.

Automatic translation from natural language descriptions into programs is a long-standing challenging problem. In this work, we consider a simple yet important sub-problem: translation from textual descriptions to If-Then programs. We devise a novel neural network architecture for this task which we train end-to-end. Specifically, we introduce Latent Attention, which computes multiplicative weights for the words in the description in a two-stage process with the goal of better leveraging the natural language structures that indicate the relevant parts for predicting program elements. Our architecture reduces the error rate by 28.57% compared to prior art. We also propose a one-shot learning scenario of If-Then program synthesis and simulate it with our existing dataset. We demonstrate a variation on the training procedure for this scenario that outperforms the original procedure, significantly closing the gap to the model trained with all data.

The determinantal point process (DPP) is an elegant probabilistic model of repulsion with applications in various machine learning tasks including summarization and search. However, the maximum a posteriori (MAP) inference for DPP which plays an important role in many applications is NP-hard, and even the popular greedy algorithm can still be too computationally expensive to be used in large-scale real-time scenarios. To overcome the computational challenge, in this paper, we propose a novel algorithm to greatly accelerate the greedy MAP inference for DPP. In addition, our algorithm also adapts to scenarios where the repulsion is only required among nearby few items in the result sequence. We apply the proposed algorithm to generate relevant and diverse recommendations. Experimental results show that our proposed algorithm is significantly faster than state-of-the-art competitors, and provides a better relevance-diversity trade-off on several public datasets, which is also confirmed in an online A/B test.

Online portfolio selection is a sequential decision-making problem in which a learner repetitively selects a portfolio over a set of assets, aiming to maximize long-term return. In this paper, we study the problem with the cardinality constraint that the number of assets in a portfolio is restricted to be at most k, and consider two scenarios: (i) in the full-feedback setting, the learner can observe price relatives (rates of return to cost) for all assets, and (ii) in the bandit-feedback setting, the learner can observe price relatives only for invested assets. We propose efficient algorithms for these scenarios that achieve sublinear regrets. We also provide regret (statistical) lower bounds for both scenarios which nearly match the upper bounds when k is a constant. In addition, we give a computational lower bound which implies that no algorithm maintains both computational efficiency, as well as a small regret upper bound.

In modern applications such as ECG monitoring, neuroimaging, wearable sensing, and industrial equipment diagnostics, complex and continuously structured data are ubiquitous, presenting both challenges and opportunities for functional data analysis. However, existing methods face a critical trade-off: conventional functional models are limited by linearity, whereas deep learning approaches lack interpretable region selection for sparse effects. To bridge these gaps, we propose a sparse Bayesian functional deep neural network (sBayFDNN). It learns adaptive functional embeddings through a deep Bayesian architecture to capture complex nonlinear relationships, while a structured prior enables interpretable, region-wise selection of influential domains with quantified uncertainty. Theoretically, we establish rigorous approximation error bounds, posterior consistency, and region selection consistency. These results provide the first theoretical guarantees for a Bayesian deep functional model, ensuring its reliability and statistical rigor. Empirically, comprehensive simulations and real-world studies confirm the effectiveness and superiority of sBayFDNN. Crucially, sBayFDNN excels in recognizing intricate dependencies for accurate predictions and more precisely identifies functionally meaningful regions, capabilities fundamentally beyond existing approaches.

We develop a finite-sample, design-based theory for random forests in which each tree is a randomized conditional predictor acting on fixed covariates and the forest is their Monte Carlo average. An exact variance identity separates Monte Carlo error from a covariance floor that persists under infinite aggregation. The floor arises through two mechanisms: observation reuse, where the same training outcomes receive weight across multiple trees, and partition alignment, where independently generated trees discover similar conditional prediction rules. We prove the floor is strictly positive under minimal conditions and show that alignment persists even when sample splitting eliminates observation overlap entirely. We introduce procedure-aligned synthetic resampling (PASR) to estimate the covariance floor, decomposing the total prediction uncertainty of a deployed forest into interpretable components. For continuous outcomes, resulting prediction intervals achieve nominal coverage with a theoretically guaranteed conservative bias direction. For classification forests, the PASR estimator is asymptotically unbiased, providing the first pointwise confidence intervals for predicted conditional probabilities from a deployed forest. Nominal coverage is maintained across a range of design configurations for both outcome types, including high-dimensional settings. The underlying theory extends to any tree-based ensemble with an exchangeable tree-generating mechanism.

In this work, we analyze alternative effective sample size (ESS) metrics for importance sampling algorithms, and discuss a possible extended range of applications. We show the relationship between the ESS expressions used in the literature and two entropy families, the Rényi and Tsallis entropy. The Rényi entropy is connected to the Huggins-Roy's ESS family introduced in \cite{Huggins15}. We prove that that all the ESS functions included in the Huggins-Roy's family fulfill all the desirable theoretical conditions. We analyzed and remark the connections with several other fields, such as the Hill numbers introduced in ecology, the Gini inequality coefficient employed in economics, and the Gini impurity index used mainly in machine learning, to name a few. Finally, by numerical simulations, we study the performance of different ESS expressions contained in the previous ESS families in terms of approximation of the theoretical ESS definition, and show the application of ESS formulas in a variable selection problem.

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