Itcanbeshown (see [18] andthesupplementary material) thatKsEM-VROpt(n, )= KFIEMOpt(n, )= n2/3O( 1) and KsEM-VRCE (n, )= KFIEMCE (n, )= n+n2/3O( 1). SPIDER estimator employed, Proof Sketch.Whilewe

For any t 0, we have k tk c3α2τL2maxκ2maxE 10 due to either the initialization (t = 0)orA3(t)(t > 0).

Behavior Trees (BTs) are high-level controllers that are useful in a variety of planning tasks and are gaining traction in robotic mission planning. As they gain popularity in safety-critical domains, it is important to formalize their syntax and semantics, as well as verify properties for them. In this paper, we formalize a class of BTs we call Stateful Behavior Trees (SBTs) that have auxiliary variables and operate in an environment that can change over time. SBTs have access to persistent shared memory (often known as a blackboard) that keeps track of these auxiliary variables. We demonstrate that SBTs are equivalent in computational power to Turing Machines when the blackboard can store mathematical (i.e., unbounded) integers. We further identify syntactic assumptions where SBTs have computational power equivalent to finite state automata, specifically where the auxiliary variables are of finitary types. We present a domain specific language (DSL) for writing SBTs and adapt the tool BehaVerify for use with this DSL. This new DSL in BehaVerify supports interfacing with popular BT libraries in Python, and also provides generation of Haskell code and nuXmv models, the latter of which is used for model checking temporal logic specifications for the SBTs. We include examples and scalability results where BehaVerify outperforms another verification tool by a factor of 100.

In this paper we develop the randomized Sharded Bayesian Additive Regression Trees (SBT) model. We introduce a randomization auxiliary variable and a sharding tree to decide partitioning of data, and fit each partition component to a sub-model using Bayesian Additive Regression Tree (BART). By observing that the optimal design of a sharding tree can determine optimal sharding for sub-models on a product space, we introduce an intersection tree structure to completely specify both the sharding and modeling using only tree structures. In addition to experiments, we also derive the theoretical optimal weights for minimizing posterior contractions and prove the worst-case complexity of SBT.

We propose a novel generative model for time series based on Schr{\"o}dinger bridge (SB) approach. This consists in the entropic interpolation via optimal transport between a reference probability measure on path space and a target measure consistent with the joint data distribution of the time series. The solution is characterized by a stochastic differential equation on finite horizon with a path-dependent drift function, hence respecting the temporal dynamics of the time series distribution. We can estimate the drift function from data samples either by kernel regression methods or with LSTM neural networks, and the simulation of the SB diffusion yields new synthetic data samples of the time series. The performance of our generative model is evaluated through a series of numerical experiments. First, we test with a toy autoregressive model, a GARCH Model, and the example of fractional Brownian motion, and measure the accuracy of our algorithm with marginal and temporal dependencies metrics. Next, we use our SB generated synthetic samples for the application to deep hedging on real-data sets. Finally, we illustrate the SB approach for generating sequence of images.

The analysis of distributed techniques is often focused upon their efficiency, without considering their robustness (or lack thereof). Such a consideration is particularly important when devices or central servers can fail, which can potentially cripple distributed systems. When such failures arise in wireless communications networks, important services that they use/provide (like anomaly detection) can be left inoperable and can result in a cascade of security problems. In this paper, we present a novel method to address these risks by combining both flat- and star-topologies, combining the performance and reliability benefits of both. We refer to this method as "Tol-FL", due to its increased failure-tolerance as compared to the technique of Federated Learning. Our approach both limits device failure risks while outperforming prior methods by up to 8% in terms of anomaly detection AUROC in a range of realistic settings that consider client as well as server failure, all while reducing communication costs. This performance demonstrates that Tol-FL is a highly suitable method for distributed model training for anomaly detection, especially in the domain of wireless networks.

Simulation-based training (SBT) is gaining popularity as a low-cost and convenient training technique in a vast range of applications. However, for a SBT platform to be fully utilized as an effective training tool, it is essential that feedback on performance is provided automatically in real-time during training. It is the aim of this paper to develop an efficient and effective feedback generation method for the provision of real-time feedback in SBT. Existing methods either have low effectiveness in improving novice skills or suffer from low efficiency, resulting in their inability to be used in real-time. In this paper, we propose a neural network based method to generate feedback using the adversarial technique. The proposed method utilizes a bounded adversarial update to minimize a L1 regularized loss via back-propagation. We empirically show that the proposed method can be used to generate simple, yet effective feedback. Also, it was observed to have high effectiveness and efficiency when compared to existing methods, thus making it a promising option for real-time feedback generation in SBT.