Computationally intensive distributed and parallel computing is often bottlenecked by a small set of slow workers known as stragglers. In this paper, we utilize the emerging idea of ``coded computation'' to design a novel error-correcting-code inspired technique for solving linear inverse problems under specific iterative methods in a parallelized implementation affected by stragglers. Example machine-learning applications include inverse problems such as personalized PageRank and sampling on graphs. We provably show that our coded-computation technique can reduce the mean-squared error under a computational deadline constraint. In fact, the ratio of mean-squared error of replication-based and coded techniques diverges to infinity as the deadline increases. Our experiments for personalized PageRank performed on real systems and real social networks show that this ratio can be as large as $10^4$. Further, unlike coded-computation techniques proposed thus far, our strategy combines outputs of all workers, including the stragglers, to produce more accurate estimates at the computational deadline. This also ensures that the accuracy degrades ``gracefully'' in the event that the number of stragglers is large.

We train the network by adopting mean-squared error as our loss function and using the AdamW optimizer [27]withalearning rateof0.01. Specifically,wefirstapply a2-layer MLP ontheoutput ofthepositional encoding layer,and then we stack 5NeRV blocks with upscale factors 5, 3, 2, 2, 2, respectively. To be specific, on the UVG-HD benchmark, we set the number of levels as 15, the number of features per level as 2, the maximum entries per level as224, and the coarsest resolution as 16. Table 7: Decoding time ofcoordinate-based representations measured with FPS (higher isbetter).

Our result builds upon an analysis for linear stochastic approximation based on Lyapunov equations and applies to both tabular setting and with linear function approximation, provided thattheoptimal policyisunique andthealgorithms converge.

In this paper, we establish a theoretical comparison between the asymptotic mean square errors of double Q-learning and Q-learning. Our result builds upon an analysis for linear stochastic approximation based on Lyapunov equations and applies to both tabular setting or with linear function approximation, provided that the optimal policy is unique and the algorithms converge. We show that the asymptotic mean-square error of Double Q-learning is exactly equal to that of Q-learning if Double Q-learning uses twice the learning rate of Q-learning and the output of Double Q-learning is the average of its two estimators. We also present some practical implications of this theoretical observation using simulations.

Computationally intensive distributed and parallel computing is often bottlenecked by a small set of slow workers known as stragglers. In this paper, we utilize the emerging idea of ``coded computation'' to design a novel error-correcting-code inspired technique for solving linear inverse problems under specific iterative methods in a parallelized implementation affected by stragglers. Example machine-learning applications include inverse problems such as personalized PageRank and sampling on graphs. We provably show that our coded-computation technique can reduce the mean-squared error under a computational deadline constraint. In fact, the ratio of mean-squared error of replication-based and coded techniques diverges to infinity as the deadline increases. Our experiments for personalized PageRank performed on real systems and real social networks show that this ratio can be as large as $10^4$. Further, unlike coded-computation techniques proposed thus far, our strategy combines outputs of all workers, including the stragglers, to produce more accurate estimates at the computational deadline. This also ensures that the accuracy degrades ``gracefully'' in the event that the number of stragglers is large.

In this paper, we utilize the emerging idea of "coded computation" to design a novel error-correcting-code inspired technique for solving linear inverse problems under specific iterative

We address this gap by analyzing Monte-Carlo policy evaluation for LQR systems and uncover a fundamental trade-off between approximation and statistical error in value estimation.

In this paper, we establish a theoretical comparison between the asymptotic mean-squared error of Double Q-learning and Q-learning. Our result builds upon an analysis for linear stochastic approximation based on Lyapunov equations and applies to both tabular setting and with linear function approximation, provided that the optimal policy is unique and the algorithms converge.

Applications such as weather forecasting and personalized medicine demand models that output calibrated probability estimates--those representative of the true likelihood of a prediction.