Active chiral viscoelastic materials exhibit elastic responses perpendicular to the applied stresses, referred to as odd elasticity. We use a covariant formulation of viscoelasticity combined with an entropy production analysis to show that odd elast
icity is not only present in active systems but also in broad classes of passive chiral viscoelastic fluids. In addition, we demonstrate that linear viscoelastic chiral solids do require activity in order to manifest odd elastic responses. In order to model the phenomenon of passive odd viscoelasticity we propose a chiral extension of Jeffreys model. We apply our covariant formalism in order to derive the dispersion relations of hydrodynamic modes and obtain clear imprints of odd viscoelastic behavior.
In this paper, we present our initial efforts for building a code-switching (CS) speech recognition system leveraging existing acoustic models (AMs) and language models (LMs), i.e., no training required, and specifically targeting intra-sentential sw
itching. To achieve such an ambitious goal, new mechanisms for foreign pronunciation generation and language model (LM) enrichment have been devised. Specifically, we have designed an automatic approach to obtain high quality pronunciation of foreign language (FL) words in the native language (NL) phoneme set using existing acoustic phone decoders and an LSTM-based grapheme-to-phoneme (G2P) model. Improved accented pronunciations have thus been obtained by learning foreign pronunciations directly from data. Furthermore, a code-switching LM was deployed by converting the original NL LM into a CS LM using translated word pairs and borrowing statistics for the NL LM. Experimental evidence clearly demonstrates that our approach better deals with accented foreign pronunciations than techniques based on human labeling. Moreover, our best system achieves a 55.5% relative word error rate reduction from 34.4%, obtained with a conventional monolingual ASR system, to 15.3% on an intra-sentential CS task without harming the monolingual recognition accuracy.
We propose a first-order fast algorithm for the weighted max-min fair (MMF) multi-group multicast beamforming problem suitable for large-scale systems. Utilizing the optimal multicast beamforming structure obtained recently, we convert the nonconvex
MMF problem into a weight minimization problem. We show this problem is a weakly convex problem and propose using the projected subgradient algorithm (PSA) to solve it directly, avoiding the conventional method for the MMF problem that requires iteratively solving its inverse problem, which is computationally expensive. We show the convergence of PSA, although our problem is only weakly convex. A method for a suitable initial point to accelerate convergence is also presented. Simulation results show that PSA offers near-optimal performance with considerably lower computational complexity than existing methods for large-scale systems.
We consider online convex optimization (OCO) over a heterogeneous network with communication delay, where multiple workers together with a master execute a sequence of decisions to minimize the accumulation of time-varying global costs. The local dat
a may not be independent or identically distributed, and the global cost functions may not be locally separable. Due to communication delay, neither the master nor the workers have in-time information about the current global cost function. We propose a new algorithm, termed Hierarchical OCO (HiOCO), which takes full advantage of the network heterogeneity in information timeliness and computation capacity to enable multi-step gradient descent at both the workers and the master. We analyze the impacts of the unique hierarchical architecture, multi-slot delay, and gradient estimation error to derive upper bounds on the dynamic regret of HiOCO, which measures the gap of costs between HiOCO and an offline globally optimal performance benchmark.
In this paper, we propose a new state representation method, called encoding sum and concatenation (ESC), for the state representation of decision-making in autonomous driving. Unlike existing state representation methods, ESC is applicable to a vari
able number of surrounding vehicles and eliminates the need for manually pre-designed sorting rules, leading to higher representation ability and generality. The proposed ESC method introduces a representation neural network (NN) to encode each surrounding vehicle into an encoding vector, and then adds these vectors to obtain the representation vector of the set of surrounding vehicles. By concatenating the set representation with other variables, such as indicators of the ego vehicle and road, we realize the fixed-dimensional and permutation invariant state representation. This paper has further proved that the proposed ESC method can realize the injective representation if the output dimension of the representation NN is greater than the number of variables of all surrounding vehicles. This means that by taking the ESC representation as policy inputs, we can find the nearly optimal representation NN and policy NN by simultaneously optimizing them using gradient-based updating. Experiments demonstrate that compared with the fixed-permutation representation method, the proposed method improves the representation ability of the surrounding vehicles, and the corresponding approximation error is reduced by 62.2%.
The safety constraints commonly used by existing safe reinforcement learning (RL) methods are defined only on expectation of initial states, but allow each certain state to be unsafe, which is unsatisfying for real-world safety-critical tasks. In thi
s paper, we introduce the feasible actor-critic (FAC) algorithm, which is the first model-free constrained RL method that considers statewise safety, e.g, safety for each initial state. We claim that some states are inherently unsafe no matter what policy we choose, while for other states there exist policies ensuring safety, where we say such states and policies are feasible. By constructing a statewise Lagrange function available on RL sampling and adopting an additional neural network to approximate the statewise Lagrange multiplier, we manage to obtain the optimal feasible policy which ensures safety for each feasible state and the safest possible policy for infeasible states. Furthermore, the trained multiplier net can indicate whether a given state is feasible or not through the statewise complementary slackness condition. We provide theoretical guarantees that FAC outperforms previous expectation-based constrained RL methods in terms of both constraint satisfaction and reward optimization. Experimental results on both robot locomotive tasks and safe exploration tasks verify the safety enhancement and feasibility interpretation of the proposed method.
We study the local analytic classification of affine structures with logarithmic pole on complex surfaces. With this result in hand, we can get the local classification of the logarithmic parallelizable d-webs, d $ge$ 3.
State estimation is critical to control systems, especially when the states cannot be directly measured. This paper presents an approximate optimal filter, which enables to use policy iteration technique to obtain the steady-state gain in linear Gaus
sian time-invariant systems. This design transforms the optimal filtering problem with minimum mean square error into an optimal control problem, called Approximate Optimal Filtering (AOF) problem. The equivalence holds given certain conditions about initial state distributions and policy formats, in which the system state is the estimation error, control input is the filter gain, and control objective function is the accumulated estimation error. We present a policy iteration algorithm to solve the AOF problem in steady-state. A classic vehicle state estimation problem finally evaluates the approximate filter. The results show that the policy converges to the steady-state Kalman gain, and its accuracy is within 2 %.
Model information can be used to predict future trajectories, so it has huge potential to avoid dangerous region when implementing reinforcement learning (RL) on real-world tasks, like autonomous driving. However, existing studies mostly use model-fr
ee constrained RL, which causes inevitable constraint violations. This paper proposes a model-based feasibility enhancement technique of constrained RL, which enhances the feasibility of policy using generalized control barrier function (GCBF) defined on the distance to constraint boundary. By using the model information, the policy can be optimized safely without violating actual safety constraints, and the sample efficiency is increased. The major difficulty of infeasibility in solving the constrained policy gradient is handled by an adaptive coefficient mechanism. We evaluate the proposed method in both simulations and real vehicle experiments in a complex autonomous driving collision avoidance task. The proposed method achieves up to four times fewer constraint violations and converges 3.36 times faster than baseline constrained RL approaches.
Affine invariant points and maps for sets were introduced by Grunbaum to study the symmetry structure of convex sets. We extend these notions to a functional setting. The role of symmetry of the set is now taken by evenness of the function. We show t
hat among the examples for affine invariant points are the classical center of gravity of a log-concave function and its Santalo point. We also show that the recently introduced floating functions and the John- and Lowner functions are examples of affine invariant maps. Their centers provide new examples of affine invariant points for log-concave functions.
