The task is to i) predict the unknown parameters, then ii) solve the optimization problem using the predicted parameters, such that the resulting solutions are good even under true parameters.

Reinforcement learning algorithms typically consider discrete-time dynamics, even though the underlying systems are often continuous in time. In this paper, we introduce a model-based reinforcement learning algorithm that represents continuous-time dynamics using nonlinear ordinary differential equations (ODEs). We capture epistemic uncertainty using well-calibrated probabilistic models, and use the optimistic principle for exploration. Our regret bounds surface the importance of the measurement selection strategy (MSS), since in continuous time we not only must decide how to explore, but also when to observe the underlying system. Our analysis demonstrates that the regret is sublinear when modeling ODEs with Gaussian Processes (GP) for common choices of MSS, such as equidistant sampling. Additionally, we propose an adaptive, data-dependent, practical MSS that, when combined with GP dynamics, also achieves sublinear regret with significantly fewer samples. We showcase the benefits of continuous-time modeling over its discrete-time counterpart, as well as our proposed adaptive MSS over standard baselines, on several applications.

The notion of cause, as formalized by Halpern and Pearl, has been recently applied to relational databases, to characterize and compute causal explanations for query answers. In this work we consider the alternative notion of sufficient explanation. We investigate its connections with database repairs as used for dealing with inconsistent databases, and with causality-based necessary explanations. We also obtain some computational results.

We present \textsf{ModularSubsetSelection} (MSS), a new algorithm for locally differentially private (LDP) frequency estimation. Given a universe of size $k$ and $n$ users, our $\varepsilon$-LDP mechanism encodes each input via a Residue Number System (RNS) over $\ell$ pairwise-coprime moduli $m_0, \ldots, m_{\ell-1}$, and reports a randomly chosen index $j \in [\ell]$ along with the perturbed residue using the statistically optimal \textsf{SubsetSelection} (SS) (Wang et al. 2016). This design reduces the user communication cost from $Θ\bigl(ω\log_2(k/ω)\bigr)$ bits required by standard SS (with $ω\approx k/(e^\varepsilon+1)$) down to $\lceil \log_2 \ell \rceil + \lceil \log_2 m_j \rceil$ bits, where $m_j < k$. Server-side decoding runs in $Θ(n + r k \ell)$ time, where $r$ is the number of LSMR (Fong and Saunders 2011) iterations. In practice, with well-conditioned moduli (\textit{i.e.}, constant $r$ and $\ell = Θ(\log k)$), this becomes $Θ(n + k \log k)$. We prove that MSS achieves worst-case MSE within a constant factor of state-of-the-art protocols such as SS and \textsf{ProjectiveGeometryResponse} (PGR) (Feldman et al. 2022) while avoiding the algebraic prerequisites and dynamic-programming decoder required by PGR. Empirically, MSS matches the estimation accuracy of SS, PGR, and \textsf{RAPPOR} (Erlingsson, Pihur, and Korolova 2014) across realistic $(k, \varepsilon)$ settings, while offering faster decoding than PGR and shorter user messages than SS. Lastly, by sampling from multiple moduli and reporting only a single perturbed residue, MSS achieves the lowest reconstruction-attack success rate among all evaluated LDP protocols.

Reinforcement learning algorithms typically consider discrete-time dynamics, even though the underlying systems are often continuous in time.

Musical (MSS) source separation of western popular music using non-causal deep learning can be very effective. In contrast, MSS for classical music is an unsolved problem. Classical ensembles are harder to separate than popular music because of issues such as the inherent greater variation in the music; the sparsity of recordings with ground truth for supervised training; and greater ambiguity between instruments. The Cadenza project has been exploring MSS for classical music. This is being done so music can be remixed to improve listening experiences for people with hearing loss. To enable the work, a new database of synthesized woodwind ensembles was created to overcome instrumental imbalances in the EnsembleSet. For the MSS, a set of ConvTasNet models was used with each model being trained to extract a string or woodwind instrument. ConvTasNet was chosen because it enabled both causal and non-causal approaches to be tested. Non-causal approaches have dominated MSS work and are useful for recorded music, but for live music or processing on hearing aids, causal signal processing is needed. The MSS performance was evaluated on the two small datasets (Bach10 and URMP) of real instrument recordings where the ground-truth is available. The performances of the causal and non-causal systems were similar. Comparing the average Signal-to-Distortion (SDR) of the synthesized validation set (6.2 dB causal; 6.9 non-causal), to the real recorded evaluation set (0.3 dB causal, 0.4 dB non-causal), shows that mismatch between synthesized and recorded data is a problem. Future work needs to either gather more real recordings that can be used for training, or to improve the realism and diversity of the synthesized recordings to reduce the mismatch...

XX, XXXX 2017 1 Direct Data Driven Control Using Noisy Measurements Ramin Esmzad, Gokul S. Sankar, T eawon Han, Hamidreza Modares, Senior, IEEE Abstract -- This paper presents a novel direct data-driven control framework for solving the linear quadratic regulator (LQR) under disturbances and noisy state measurements. The system dynamics are assumed unknown, and the LQR solution is learned using only a single trajectory of noisy input-output data while bypassing system identification. Our approach guarantees mean-square stability (MSS) and optimal performance by leveraging convex optimization techniques that incorporate noise statistics directly into the controller synthesis. First, we establish a theoretical result showing that the MSS of an uncertain data-driven system implies the MSS of the true closed-loop system. Building on this, we develop a robust stability condition using linear matrix inequalities (LMIs) that yields a stabilizing controller gain from noisy measurements. Finally, we formulate a data-driven LQR problem as a semidefinite program (SDP) that computes an optimal gain, minimizing the steady-state covariance. Extensive simulations on benchmark systems--including a rotary inverted pendulum and an active suspension system--demonstrate the superior robustness and accuracy of our method compared to existing data-driven LQR approaches. The proposed framework offers a practical and theoretically grounded solution for controller design in noise-corrupted environments where system identification is infeasible. I NTRODUCTION D IRECT data-driven control has recently gained a surge of interest due to its control-oriented approach to solving control design problems [1]-[3]. That is, controller parameters are learned directly using input-output or input-state trajectories, without explicitly constructing a predictive model of the system. Bypassing system identification allows for leveraging the collected data to achieve what is best for the control objectives rather than using the data to fit a predictive model.