Video streaming over cooperative wireless networks We study the problem of broadcasting video streams over a WMAN to many mobile devices. We propose to form a cooperative network among mobile devices that receive the same video stream, and share received video data over a WLAN. The proposed system significantly reduces the energy consumption and the channel switching delay. We design a distributed leader election algorithm for the cooperative system and analytically show that the proposed system outperforms current systems in terms of energy consumption and channel switching delay. We evaluate the proposed system in a real mobile video streaming testbed as well as in a trace driven simulator. Our experimental results show that the proposed system: (i) achieves as high as 70% of energy saving gain, (ii) outperforms current systems with only three cooperative mobile devices, (iii) reduces channel switching delay by up to 98%, (iv) is robust under device failures and quickly reacts to network dynamics, and (v) uniformly distributes load across all cooperative devices. Mobile video streaming is starting to become a reality with the recent launch of 3G services and the significant consumer demand for multimedia content. Although music and gaming are currently dominant sources of revenue for mobile devices, the mobile TV service, which allows users to watch TV programs on the mobile devices, is catching up quickly. Furthermore, recent mobile devices in the market are equipped with fast processors, high resolution displays and multiple network interfaces so that they are powerful Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. MMSys '10, February 22-23, 2010 , Phoenix, Arizona, USA. Copyright 2010 ACM 978-1-60558-914-5/10/02 ...$10.00.. enough to natively receive, decode, and display videos sent over wireless networks. The capabilities of the mobile devices as well as the users' desire to access multimedia content anywhere and at anytime have created a strong demand for mobile TV services. Supporting mobile TV natively is also an attractive selling point for mobile device manufacturers.. Videos can be sent to mobile devices either over cellular networks or dedicated broadcast networks. Cellular networks cannot concurrently support a large number of mobile devices, as they are designed for unicast and have limited bandwidth. In addition, expanding a cellular network for higher capacity to accommodate more users is expensive. In contrast, in a Wireless Metropolitan Area Network (WMAN), a base station can broadcast videos to support a large number of mobile devices within its coverage range. Streaming videos over WMANs is promising as it supports more mobile devices with lower cost on network infrastructure. We consider video streaming over WMANs in this work.. Streaming videos to mobile devices is challenging, because mobile devices are battery powered and have stringent energy constraints. Therefore, energy saving on mobile devices is important since lower energy consumption leads to longer watch time and increases the user satisfaction. Current video streaming systems use WMANs to broadcast videos, in which each mobile device independently receives and decodes the video data from the base station. That is, every bit of data is used at most once before being discarded. In this paper, we explore the potential of better utilizing the received video data by sharing it among several mobile devices that watch the same video stream. More precisely, we propose a new video streaming system in which several mobile devices receive and cache video streams broadcast in a WMAN and share the received data over a Wireless Local Area Network (WLAN). Such sharing is possible as WLANs are very popular and many access points are readily available. Furthermore, our proposed cooperative system supports the ad-hoc mode of WLAN in case there is no access point available.. We explore the benefits of organizing mobile devices into cooperative networks in video broadcast systems. We propose a cooperative system that consists of a WMAN and a WLAN. We analytically compare this system against the current video broadcast systems that only use WMAN to distribute video streams. We show that the proposed cooperative system achieves better performance from several aspects. First, the energy consumption is reduced, because mobile devices can receive bursts from other mobile devices over the WLAN, which consumes less energy compared to receiving bursts over the WMAN. Second, the delay of mobile devices switching to new video streams can be significantly reduced (almost eliminated), because these mobile devices can request an immediate burst transmission from other devices using unicast. Our experimental results from a real testbed indicate that the proposed cooperative system is promising, because it: (i) achieves as high as 70% of energy saving gain, (ii) outperforms current systems with only three (or more) cooperative mobile devices, (iii) reduces channel switching delay by up to 98%, (iv) is robust against device failures and quickly reacts to network dynamics, and (v) uniformly distributes load on all mobile devices.. The rest of the paper is organized as follows. Section 2 presents a brief background on WMAN networks and summarizes some existing strategies on energy saving and channel switching delay reduction. In Section 3, we present our cooperative strategy to save energy and reduce channel switching delay concurrently. We numerically analyze our cooperative system in Section 4. We present the experimental results from our testbed in Section 5, and we present the simulation based evaluation in Section 6. We conclude the paper in Section 7. We consider a video broadcast system with multiple mobile devices as receivers, where each mobile device joins a WMAN and a WLAN as illustrated in Fig. 2 . The base station of this WMAN concurrently broadcasts multiple video streams to all mobile devices. These video streams are sent in bursts to save energy. Burst transmission, however, increases the channel switching delay. In WMAN only network, there exists a tradeoff between energy saving and channel switching delay because for a particular video channel, we save more energy by increasing the burst size in order to sleep for a longer time. However, as shown in Fig. 2(a) during the sleep time of a TV channel, no data is transmitted such that a new joiner of that channel needs to wait for a longer time to get the next burst data. This increases the channel switching delay for the new joiner. While the WMAN covers a much larger area compared to the WLAN, receiving video data from the WMAN may consume more energy than receiving from the WLAN. This is because a WLAN covers fewer mobile devices, and thus is less sensitive to path loss, shadowing, and interference. Therefore, broadcasting video streams over the WLAN achieves higher transmission rates than over the WMAN. As shown in Fig. 2(b) , transmitting the same video stream over WLANs at higher rates leads to shorter transmission time, and allows mobile devices to turn off the wireless receivers for longer time, thus reduces energy consumption.. As shown in Fig. 2(c) , we propose to form a cooperative network among all mobile devices that are viewing the same video stream. We let N be the size of the cooperative network. We then run a leadership protocol among these N mobile devices to elect one device that is on-duty. The onduty device receives data bursts from the WMAN base station, and relays the data bursts to other mobile devices via WLAN. K backups devices are also elected, which monitor the status of the on-duty device and initiate a switch-over if the on-duty device fails or leaves the cooperative network. All other N -K -1 devices are off-duty mobile devices, which receive the data bursts over the WLAN from the on-duty device. Last, the on-duty device offers the most recent burst to mobile devices that join this cooperative network. This allows new mobile devices to start playing out faster, as they do not need to wait for the next broadcast burst in WMAN. Both the infrastructure mode and ad-hoc mode in WLAN are supported in our cooperative system. The former mode requires an access point (AP). Many access points are readily available these days in places such as universities, airports, restaurants, and coffee shops. The latter mode does not require any infrastructure and it allows mobile devices to form a cooperative network in an ad-hoc manner. This ad-hoc mode is useful when no APs are available or are not freely accessible. For example, mobile users watching video streams while traveling on a bus or train could form a mobile ad-hoc network (MANET) to benefit from the proposed system to save energy and reduce channel switching delay. The support of the ad-hoc mode significantly lowers down the requirement of using our cooperative system. Additional operations such as unique IP assignment and multicast routing setup are required to form the cooperative group in MANET due to the lack of access point. We discuss these extra operations in [6] due to space limitations. We note that if the mobile devices already form a MANET to support other distributed applications, our cooperative video streaming system can easily use this MANET and there will be no need to duplicate the operations described below. In most cases, however, the MANET does not exist. We studied the problem of broadcasting video streams over a WMAN to mobile devices. We proposed a cooperative system in which several mobile devices share received video data bursts over a WLAN. The proposed system reduces the energy consumption and significantly reduces the channel switching delay. We analytically showed that the proposed cooperative system outperforms current system in terms of the energy consumption with only few cooperative devices.. We presented a simple distributed leader election algorithm to choose the on-duty and backup devices in the cooperative network. The proposed algorithm imposes very little computation and communication overheads. Moreover the proposed algorithm enables truthful cooperation among devices because it distributes the load by rotating the onduty role across all devices. The on-duty device is elected based on previous contributions, where the contribution of a device is not computed by itself but computed independently by all other devices based on the actual data received from the on-duty device. Therefore the room for a device to cheat or free-ride is very limited.. Our experimental results from the real testbed showed that the proposed cooperative system is promising, because it achieves high energy saving, significantly reduces the channel switching delay and uniformly distributes load on all mobile devices. Furthermore, we complemented our evaluation in the testbed by several simulations that address larger networks, device failures, departures and mobility. Our simulations confirm the viability of the proposed cooperative system and the significant energy saving potential that can be achieved by using our simple algorithm. Some previous works explore the benefits of using cooperative network between WMANs and WLANs. Pei et al. [5] develop an analytical model in the cooperative network to evaluate the call block probability and throughput performance. They also propose two cooperative load-balancing strategies in order to improve the resource utilization. Niyato and Hossain [7] propose a hierarchical bandwidth management scheme using game theory to achieve fairness and efficiency of radio resource allocation. The optimal burst size for WMAN and WLAN connections can be determined by their proposed two-level hierarchical model. Pan et al. [8] propose a quantitative evaluation of the effect of integrating WiMAX and WiFi networks, as compared to WiMAX or WiFi only systems. Their cooperative network is used to evaluate the VoIP traffic as well as the corresponding resource management scheme on WiFi to WiMAX handover. However, to the best of our knowledge, none of the previous works addresses the video broadcast over the cooperative WMAN and WLAN networks.. A number of previous works address the energy saving problems in WMANs only network. Due to the time slicing nature of WMANs, energy saving of mobile devices can be done by burst scheduling on the base station side. Yang et al. [9] address the effectiveness of the time slicing technique for given burst schedules and calculate the corresponding energy saving level. This work does not solve the server side burst scheduling problem. Balaguer et al. [10] propose an energy saving strategy by not receiving some MPE-FEC (Multiprotocol Encapsulation -Forward Error Correction) sections once the sections received are good enough to reconstruct the data. Dropping some MPE-FEC sections can help mobile devices turn off their RF circuits earlier for additional energy saving. Hefeeda and Hsu [11] prove that the general burst scheduling problem with arbitrary bit rates of TV channels is NP-complete. They then propose a practical simplification of the general problem, which allows the bit rates of the TV channels to have power of 2 increments. The running time of this simplification is O(S log S) where S is the total number of TV channels. Hsu and Hefeeda [12] address the general scheduling problem where each TV channel can take any arbitrary bit rate, which enables finer-grained optimization by providing higher bit rate flexibility. All the above works are orthogonal to ours, because they assume all mobile devices receive video data from their WMAN interfaces only, while our work considers sharing video data over a WLAN in order to save energy beyond what can be saved by time slicing.. Some previous works address the channel switching delay problem in WMANs only network. Channel switching delay refers to the time period between when a user switches to a new video stream until his/her mobile device starts rendering that stream. Channel switching delay consists of several components [13] , including time slicing delay, frame refresh delay, decoder buffering delay and reception delay. Time slicing delay is a dominant component among them, which is the time period between the mobile device tunes to a new video stream until the first burst of that video stream arrives. We only consider time slicing delay in this work, and assume other delay components are constant as they are not impacted by the proposed cooperative system. Hsu and Hefeeda [14] propose to control the channel switching delay by simulcasting each video over two streams. In contrast, our work uses unicast over a WLAN to almost eliminate the channel switching delay.

B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O B I O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O B I O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Learning via finitely many queries This work introduces a new query inference model that can access data and communicate with the teacher by asking finitely many Boolean queries in a language L. In this model the parameters of interest are the number of queries used and the expressive power of L. We study how the learning power varies with these parameters. Results suggest that this model may help studying query inference in a resource bounded environment. Formal learning models are designed for rigorous studies on issues such as language acquisition, empirical inquiry of knowledge, etc. that are relevant to human and machine learning [18] . In Angluin's teacher and learner paradigm [1, 2] , the learner's task is to identify an unknown concept via queries to the teacher, who provides information about the target concept the learner wishes to learn. Consider the example shown in figure 1 , where the learner can observe data as well as asking questions.. In this model, we will refer the information received from the teacher as additional information. A number of basic questions arise. For example, one may ask:. (a) What types of additional information can the learner receive from the teacher? (b) How much additional information can the learner receive from the teacher?. The answers usually depend on the types of queries used and the number of queries allowed. In this paper we will consider these questions within the computability theoretic framework [13, 17] . We will introduce the background of the computability theoretic approach in section 1.1.. In our model, additional information obtained from the teacher are the answers to the questions the learner posted. We will restrict our attention to Boolean questions formulated in a language L. One may think of these additional information as a collection (possibly infinite) of properties that the learner is unaware of but is simple enough so that the learner can formulate the questions in L. The teacher is assumed to know the correct answers to any properties that can be formulated in L. While the teacher in our model is, in general, non-algorithmic, this approach can provide some insights to learning. For example, suppose that a concept can be learned by asking at most 3 Boolean queries. Then, it is theoretically possible that one can enumerate a list of 2 3 Turing machines where at least one of them can learn the concept. However, it may not be possible to decide which machine from the eight of them. In this work we will put an emphasis on the number of queries used in the learning process and the languages used to formulate the queries.. Many major developments in research on computability-theoretic learning theory and query inference are omitted here. The readers are strongly encouraged to consult references such as [4, 7, 14, 16, 18, 23] and the materials cited therein for a better view of this subject.. There has been much progress in related learning models. For readers who are interested in learning via queries formulated in the setting where the concept class and the problem domain are finite, we referred them to the excellent survey [3] and the references cited therein for a thorough view in that area. For readers who are interested in other resource bounded models formulated in an computability-theoretic setting, we refer them to the related literature, such as [5, 6, 10, 11] .

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Trading Regret for Efficiency: Online Convex Optimization with Long Term Constraints In this paper we propose efficient algorithms for solving constrained online convex optimization problems. Our motivation stems from the observation that most algorithms proposed for online convex optimization require a projection onto the convex set K from which the decisions are made. While the projection is straightforward for simple shapes (e.g., Euclidean ball), for arbitrary complex sets it is the main computational challenge and may be inefficient in practice. In this paper, we consider an alternative online convex optimization problem. Instead of requiring that decisions belong to K for all rounds, we only require that the constraints, which define the set K, be satisfied in the long run. By turning the problem into an online convex-concave optimization problem, we propose an efficient algorithm which achieves O( √ T ) regret bound and O(T 3/4 ) bound on the violation of constraints. Then, we modify the algorithm in order to guarantee that the constraints are satisfied in the long run. This gain is achieved at the price of getting O(T 3/4 ) regret bound. Our second algorithm is based on the mirror prox method (Nemirovski, 2005) to solve variational inequalities which achieves O(T 2/3 ) bound for both regret and the violation of constraints when the domain K can be described by a finite number of linear constraints. Finally, we extend the results to the setting where we only have partial access to the convex set K and propose a multipoint bandit feedback algorithm with the same bounds in expectation as our first algorithm. Online convex optimization has recently emerged as a primitive framework for designing efficient algorithms for a wide variety of machine learning applications (Cesa-Bianchi and Lugosi, 2006) . In general, an online convex optimization problem can be formulated as a repeated game between a learner and an adversary: at each iteration t, the learner first presents a solution x t ∈ K, where K ⊆ R d is a convex domain representing the solution space; it then receives a convex function f t (x) : K → R + and suffers the loss f t (x t ) for the submitted solution x t . The objective of the learner is to generate a sequence of solutions x t ∈ K, t = 1, 2, · · · , T that minimizes the regret R T defined as. (1). Regret measures the difference between the cumulative loss of the learner's strategy and the minimum possible loss had the sequence of loss functions been known in advance and the learner could choose the best fixed action in hindsight. When R T is sub-linear in the number of rounds, that is, o(T ), we call the solution Hannan consistent (Cesa-Bianchi and Lugosi, 2006) , implying that the learner's average per-round loss approaches the average per-round loss of the best fixed action in hindsight. It is noticeable that the performance bound must hold for any sequence of loss functions, and in particular if the sequence is chosen adversarially. Many successful algorithms have been developed over the past decade to minimize the regret in the online convex optimization. The problem was initiated in the remarkable work of Zinkevich (2003) which presents an algorithm based on gradient descent with projection that guarantees a regret of O( √ T ) when the set K is convex and the loss functions are Lipschitz continuous within the domain K. In and Shalev-Shwartz and Kakade (2008) algorithms with logarithmic regret bound were proposed for strongly convex loss functions. In particular, the algorithm in is based on online Newton step and covers the general class of exp-concave loss functions. Notably, the simple gradient based algorithm also achieves an O(log T ) regret bound for strongly convex loss functions with an appropriately chosen step size. Bartlett et al. (2007) generalizes the results in previous works to the setting where the algorithm can adapt to the curvature of the loss functions without any prior information. A modern view of these algorithms casts the problem as the task of following the regularized leader (Rakhlin, 2009 ). In Abernethy et al. (2009) , using game-theoretic analysis, it has been shown that both O( √ T ) for Lipschitz continuous and O(log T ) for strongly convex loss functions are tight in the minimax sense.. Examining the existing algorithms, most of the techniques usually require a projection step at each iteration in order to get back to the feasible region. For the performance of these online algorithms, the computational cost of the projection step is of crucial importance. To motivate the setting addressed in this paper, let us first examine a popular online learning algorithm for minimizing the regret R T based on the online gradient descent (OGD) method (Zinkevich, 2003) . At each iteration t, after receiving the convex function f t (x), the learner computes the gradient ∇f t (x t ) and updates the solution x t by solving the following optimization problem x t+1 = Π K (x t − η∇f t (x t )) = arg min. where Π K (·) denotes the projection onto K and η > 0 is a predefined step size. Despite the simplicity of the OGD algorithm, the computational cost per iteration is crucial for its applicability. For general convex domains, solving the optimization problem in (2) is an offline convex optimization problem by itself and can be computationally expensive. For example, when one envisions a positive semidefinitive cone in applications such as distance metric learning and matrix completion, the full eigen-decomposition of a matrix is required to project the updated solutions back into the cone. Recently several efficient algorithms have been developed for projection onto specific domains, for example, ℓ 1 ball (Duchi et al., 2008; Liu and Ye, 2009) ; however, when the domain K is complex, the projection step is a more involved task or computationally burdensome.. To tackle the computational challenge arising from the projection step, we consider an alternative online learning problem. Instead of requiring x t ∈ K, we only require the constraints, which define the convex domain K, to be satisfied in a long run. Then, the online learning problem becomes a task to find a sequence of solutions x t , t ∈ [T ] that minimizes the regret defined in (1), under the long term constraints, that is, T t=1 x t /T ∈ K. We refer to this problem as online learning with long term constraints. In other words, instead of solving the projection problem in (2) on each round, we allow the learner to make decisions at some iterations which do not belong to the set K, but the overall sequence of chosen decisions must obey the constraints at the end by a vanishing convergence rate.. From a different perspective, the proposed online optimization with long term constraints setup is reminiscent of regret minimization with side constraints or constrained regret minimization addressed in Mannor and Tsitsiklis (2006) , motivated by applications in wireless communication. In regret minimization with side constraints, beyond minimizing regret, the learner has some side constraints that need to be satisfied on average for all rounds. Unlike our setting, in learning with side constraints, the set K is controlled by adversary and can vary arbitrarily from trial to trial. It has been shown that if the convex set is affected by both decisions and loss functions, the minimax optimal regret is generally unattainable online (Mannor et al., 2009) .. One interesting application of the constrained regret minimization is multi-objective online classification where the learner aims at simultaneously optimizing more than one classification performance criteria. In the simple two objective online classification considered in Bernstein et al. (2010) , the goal of the online classifier is to maximize the average true positive classification rate with an additional performance guarantee in terms of the false positive rate. Following the Neyman-Pearson risk, the intuitive approach to tackle this problem is to optimize one criterion (i.e., maximizing the true positive rate) subject to explicit constraint on the other objective (i.e., false positive rate) that needs to be satisfied on average for the sequence of decisions. The constrained regret matching (CRM) algorithm, proposed in Bernstein et al. (2010) , efficiently solves this problem by relaxing the objective under mild assumptions on the single-stage constraint. The main idea of the CRM algorithm is to incorporate the penalty, that should be paid by the learner to satisfy the constraint, in the objective (i.e., true positive rate) by subtracting a positive constant at each decision step. It has been shown that the CRM algorithm asymptotically satisfies the average constraint (i.e., false positive rate) provided that the relaxation constant is above a certain threshold.. Finally, it is worth mentioning that the proposed setting can be used in certain classes of online learning such as online-to-batch conversion (Cesa-Bianchi et al., 2004) , where it is sufficient to guarantee that constraints are satisfied in the long run. More specifically, under the assumption that received examples are i.i.d samples, the solution for batch learning is to average the solutions obtained over all the trials. As a result, if the long term constraint is satisfied, it is guaranteed that the average solution will belong to the domain K.. In this paper, we describe and analyze a general framework for solving online convex optimization with long term constraints. We first show that a direct application of OGD fails to achieve a sub-linear bound on the violation of constraints and an O( √ T ) bound on the regret. Then, by turning the problem into an online convex-concave optimization problem, we propose an efficient algorithm which is an adaption of OGD for online learning with long term constraints. The proposed algorithm achieves the same O( √ T ) regret bound as the general setting and O(T 3/4 ) bound for the violation of constraints. We show that by using a simple trick we can turn the proposed method into an algorithm which exactly satisfies the constraints in the long run by achieving O(T 3/4 ) regret bound. When the convex domain K can be described by a finite number of linear constraints, we propose an alternative algorithm based on the mirror prox method (Nemirovski, 2005) , which achieves O(T 2/3 ) bound for both regret and the violation of constraints. Our framework also handles the cases when we do not have full access to the domain K except through a limited number of oracle evaluations. In the full-information version, the decision maker can observe the entire convex domain K, whereas in a partial-information (a.k.a bandit setting) the decision maker may only observe the cost of the constraints defining the domain K at limited points. We show that we can generalize the proposed OGD based algorithm to this setting by only accessing the value oracle for domain K at two points, which achieves the same bounds in expectation as the case that has a full knowledge about the domain K. In summary, the present work makes the following contributions:. • A general theorem that shows, in online setting, a simple penalty based method attains linear bound O(T ) for either the regret or the long term violation of the constraints and fails to achieve sub-linear bound for both regret and the long term violation of the constraints at the same time.. • A convex-concave formulation of online convex optimization with long term constraints, and an efficient algorithm based on OGD that attains a regret bound of O(T 1/2 ), and O(T 3/4 ) violation of the constraints.. • A modified OGD based algorithm for online convex optimization with long term constraints that has no constraint violation but O(T 3/4 ) regret bound.. • An algorithm for online convex optimization with long term constraints based on the mirror prox method that achieves O(T 2/3 ) regret and constraint violation.. • A multipoint bandit version of the basic algorithm with O(T 1/2 ) regret bound and O(T 3/4 ) violation of the constraints in expectation by accessing the value oracle for the convex set K at two points.. The remainder of the paper is structured as follows: In Section 3, we first examine a simple penalty based strategy and show that it fails to attain sub-linear bound for both regret and long term violation of the constraints. Then, we formulate regret minimization as an online convex-concave optimization problem and apply the OGD algorithm to solve it. Our first algorithm allows the constraints to be violated in a controlled way. It is then modified to have the constraints exactly satisfied in the long run. Section 4 presents our second algorithm which is an adaptation of the mirror prox method. Section 5 generalizes the online convex optimization with long term constraints problem to the setting where we only have a partial access to the convex domain K. Section 6 concludes the work with a list of open questions. In this study we have addressed the problem of online convex optimization with constraints, where we only need the constraints to be satisfied in the long run. In addition to the regret bound which is the main tool in analyzing the performance of general online convex optimization algorithms, we defined the bound on the violation of constraints in the long term which measures the cumulative violation of the solutions from the constraints for all rounds. Our setting is applied to solving online convex optimization without projecting the solutions onto the complex convex domain at each iteration, which may be computationally inefficient for complex domains. Our strategy is to turn the problem into an online convexconcave optimization problem and apply online gradient descent algorithm to solve it. We have proposed efficient algorithms in three different settings; the violation of constraints is allowed, the constraints need to be exactly satisfied, and finally we do not have access to the target convex domain except it is bounded by a ball. Moreover, for domains determined by linear constraints, we used the mirror prox method, a simple gradient based algorithm for variational inequalities, and obtained an O(T 2/3 ) bound for both regret and the violation of the constraints.. Our work leaves open a number of interesting directions for future work. In particular it would be interesting to see if it is possible to improve the bounds obtained in this paper, i.e., getting an O( √ T ) bound on the regret and better bound than O(T 3/4 ) on the violation of constraints for general convex domains. Proving optimal lower bounds for the proposed setting also remains as an open question. Also, it would be interesting to consider strongly convex loss or constraint functions. Finally, relaxing the assumption we made to exactly satisfy the constraints in the long run is an interesting problem to be investigated.

O O O O B I I O O O O O O O O O O O O O O B I I O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Choquet boundaries and efficiency This research paper is devoted to establish the coincidence between Choquet boundaries and a new type of approximate efficient points sets in ordered Hausdorff locally convex spaces, being based on the first result established by us concerning such a property as this for Pareto-type efficient points sets and the corresponding Choquet boundaries of non-empty compact sets, with respect to appropriate convex cones of real, increasing and continuous functions. Thus, the main result represents a strong connection between two great fields of mathematics: The Axiomatic Theory of Potential and Vector Optimization. The present study contains also important relationships concerning strong optimization and approximate efficiency, interesting examples, pertinent remarks and some open problems. The Choquet boundary is an important concept in the Axiomatic Theory of Potentials, while efficiency is a fundamental notion in Vector Optimization. The main aim of this work is to generalize our coincidence result given in [7] between the set of all Pareto-type minimum points of any non-empty, compact set in an ordered Hausdorff locally convex space and the Choquet boundary of the same set with respect to the convex cone of all real, increasing and continuous functions defined on the set, using an appropriate and new concept of approximate efficiency. The paper is organized as follows: Section 2 is devoted to the Choquet boundary and its immediate properties presented in an original manner; it contains some important links between this notion and Altomare projections and relevant examples on Choquet boundaries. In Section 3, we define the approximate efficiency, we show how this notion is related to: Pareto-type efficiency, the fixed points of multifunctions and the strong optimisation, and we give the principal theorem. Both these sections are completed with significant remarks. Section 4 concludes the paper with some open problems. All the elements of ordered topological vector spaces used in this work are in accordance with [28] .

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Combined Data-driven and Event-driven Scheduling Technique for Fast Distributed Cosimulation Abstract-Fast distributed cosimulation is a challenging problem for the embedded system design. The main theme of this paper is to increase the simulation speed by reducing the frequency of inter-simulator communications, reducing the active duration of simulators, and utilizing the parallelism of component simulators. Those enhancements are accomplished by the proposed virtual synchronization technique which combines event-driven and data-driven simulation methods. Experimental results show that the proposed technique can boost the cosimulation speed significantly compared with the previous conservative approaches. As the embedded systems are complex and the design turn-around time is shortened, the performance of co-simulation becomes more important to verify such a system. And the component simulators used in the cosimulation are likely to be heterogeneous or geographically distributed. So the fast distributed cosimulation is essential for the embedded system design.. Our proposed backplane approach uses the "deadlock detection and recovery" approach to enhance the parallel execution of component simulators. The key contribution of the proposed approach is to combine data-driven and event-driven simulation technique for fast distributed cosimulation. Data-driven properties of the specification model reduce the number of communication packet exchanges by message grouping and minimize time-synchronization overhead by the virtual synchronization. Virtual synchronization also reduces the active duration of component simulators significantly. The experiments give promising results on the performance improvement specially when there are more component simulators involved.

O O O O O O O O O B O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O B I B I O O O O O O O O O O O O O O O O O O O O O O O O O O


Fat-shattering and the learnability of real-valued functions We consider the problem of learning real-valued functions from random examples when the function values are corrupted with noise. With mild conditions on independent observation noise, we provide characterizations of the learnability of a real-valued function class in terms of a generalization of the Vapnik-Chervonenkis dimension, the fat-shattering function, introduced by Kearns and Schapire. We show that, given some restrictions on the noise, a function class is learnable in our model if and only if its fat-shattering function is finite. With different (also quite mild) restrictions, satisfied for example by gaussian noise, we show that a function class is learnable from polynomially many examples if and only if its fatshattering function grows pol ynomially. We prove analogous results in an agnostic setting, where there is no assumption of an underlying function class. In many common definitions of learning, a learner sees a sequence of values of an unknown function at random points, and must, with high probability, choose an accurate approximation to that function.. The function is assumed to be a member of some known class. Using a popular definition of the problem of learning {O, 1}-valued functions (probably approximately correct learning -see [9] , [22] ), Blumer, Ehrenfeucht, Haussler, and Warmuth have shown [9] that the Vapnik-Chemonenkis dimension (see [23] ) of a function class characterizes its learnability, in the sense that a function class is learnable if and only if its Vapnik-Chervonenkis dimension is finite. Natarajan [15] and Ben-David, Cesa-Bianchi, Haussler and Long [7] have characterized the learnability of Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright tIOtiC8 and the title of the publication and its date appear, and notice is given that copying is by permission of the Association of Computing Machinery, To copy otherwise, or to republish, requires a fee and/or specific permission. COLT 94-7/94 New Brunswick, N..J. USA @ 1994 ACM 0-89791 -655-7/94/0007..$3.50 {O, .... n}-valued functions for fixed n. Alon, Ben-David, Cesa-Bianchi, and Haussler have proved an analogous result for the problem of learning probabilistic concepts [1] . In this case, there is an unknown [0, I]-valued function, but the learner does not receive a sequence of values of the function at random points. Instead, with each random point it sees either O or 1, with the probability of a 1 given by the value of the unknown function at that point. Kearns and Schapire [12] introduced a generalization of the Vapnik-Chervonenkis dimension, which we call the fat-shattering function, and showed that a class of probabilistic concepts is learnable only if the class has a finite fat-shattering function. The main learning result of [1] is that finiteness of the fat-shattering function of a class of probabilistic concepts is also sufficient for learnability.. In this paper, we consider the learnability of [0, 1]-valued function classes. We show that a class of [0, 1]-valued functions is learnable from a finite training sample with observation noise satisfying some mild conditions (the distribution has bounded support and its density satisfies a smoothness constraint) if and only if the class has a finite fat-shattering function.. We also consider small-sample learnability, for which the sample size is allowed to grow only polynornially with the required performance parameters.. We show that a real-valued function class is learnable from a small sample with observation noise satisfying some other quite mild conditions (the distribution need not have bounded support, but it must have light tails and be symmetric about zero; gaussian noise satisfies these conditions) if and only if the fat-shattering function of the class has a polynomial rate of growth.. We also consider agnostic learning [11] [13], in which there is no assumption of an underlying function generating the training examples, and the performance of the learning algorithm is measured by comparison with some function class F. We show that the fat-shattering function of F characterizes finite-sample and small-sample learnability in this case also.. The proof of the lower bound on the number of examples necessary for learning is in two steps. First, we show that the problem of learning real-valued functions in the presence of noise is not much easier than that of leaning functions in a discrete-vrducd function class obtained by quantizing the real-valued function class. This formalizes the intuition that a noisy, real-valued measurement provides little more inforrna-tion than a quantized measurement, if the quantization width is sufficiently small. Existing lower bounds on the number of examples required for learning discrete-valued function classes [7] , [15] are not strong enough for our purposes. We improve these lower bounds by relating the problem of learning the quantized function class to that of learning {O, 1}-valued functions. The proof of the upper bound departs from the basic outline of proofs of related upper bounds [1], [11] in one key way (see the discussion preceding Lemma 15), and might therefore contribute a useful new technique.. In addition to the aforementioned papers, other general results about learning real-valued functions have been obtained. Haussler [11] gives sufficient conditions for agnostic learnability. provide sufficient conditions that a function that approximately interpolates the target function is a good approximation to it. Natarajan [16] considers the problem of learning a class of real-valued functions in the presence of bounded observation noise, and presents sufficient conditions for learnability.. Merhav and Feder [14] , and Auer, Long, Maass, and Woeginger [4] study function learning in a worst-case setting.. In the next section, we define admissible noise distribution classes and the learning problems, and present the characterizations of learnability.. Sections 3 and 4 give lower and upper bounds on the number of examples necessary for learning real-valued functions.. Section 5 presents the characterization of agnostic learnability. Section 6 discusses our results.

O O O O O O O O O O O O B O O O O B O O O B O O O B O O O O O O B O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O B O O B O O O O B O O O O O O O O O O O O O O O O O O O O B O O O O O B O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O B O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O B O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O B O O O O O O O B O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O B O O O O O O O O O O B O O O O O O O O O O O O O O O B O O O O O B O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O B O O O O O O O O O O O B O O O O O O B O O O O O O O O O O O O O B O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O B O O O O O O O O O O O O O O O O O O O O O O O B O O O B O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O B O O O O B O O O O O O O O O O O O O O O O O O O O B O O B O O O O O O B O O O O O O O O


Three dimensional evolutionary aerodynamic design optimization with CMA-ES In this paper, we present the application of evolutionary optimization methods to a demanding, industrially relevant engineering domain, the three-dimensional optimization of gas turbine stator blades. This optimization problem is high-dimensional search and computationally very expensive. We show that, despite of its difficulty, the problem is feasible. Our approach not only successfully optimizes the aerodynamic design but also yields interesting results from an engineering point of view. The availability of relatively inexpensive, massive computing power in form of PC clusters made it possible to treat complex, computationally intensive application problems and to verify the everyday or real world suitability of Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. algorithms that hitherto were only tested on toy problems or in simplified application domains.. One of the problems on the verge of tractability even today is the three-dimensional optimization of aerodynamic designs. The difficulty of this optimization task stems on the one hand from the difficulty and high computational costs of 3D computational flow analysis and on the other hand from the fact that 3D flows are not fully understood yet.. In this paper, we present an approach to 3D aerodynamic design optimization using evolutionary strategies. We show that this approach is indeed feasible and not only successfully optimizes the aerodynamic design but also yields interesting results from an engineering point of view. The aerodynamic design that we optimize is part of a gas turbine that is used in small business jets. The main parts of a gas turbine are depicted schematically in Fig. 1 . In the current research we focus on the turbine which is composed of several rows of airfoil cascades. Some of these rows, the rotors, are connected to the central shaft of the engine and rotate at high speed thus driving the engine's fan and compressor and converting gas energy to mechanical energy. The other rows, the stators, are fixed and serve to keep the flow from spiralling around the axis. Our goal is to optimize the design of the turbine stator blades which are of a special type in our case. The stator is a so-called ultralow-aspect-ratio (ULAR) stator. This means that a stator row is made up of only 8 stator blades. This is a very small number compared to 20 -60 blades that are used in more conventional turbine designs. Fig. 2 depicts part of a ULAR stator row. The ULAR blades offer considerable benefits as compared to more conventional blades. For example, the blade resonance in the following rotor cascade is reduced. In general, however, ULAR stator blades are only rarely used in gas turbines because of their relatively poor stage efficiency that is much lower than the efficiency of the more conventional high aspect ratio turbines. The flow field of the ULAR stator that is depicted by arrows in Fig. 2 shows the reasons for the poorer performance. There is a very strong inward-radial cross flow on the blade suction side. Also the flow field near the hub-end-wall is very complicated due to the interaction of the secondary flow with the transonic main flow. As a result, the aerodynamic loss near the hub region is considerably increased as compared to the conventional highaspect-ratio blade. It is this higher loss near the hub region that prevents a further improvement of the stage efficiency. The ULAR blade flow characteristics make it unlikely that the advanced design principles developed for high aspect ratio blades will help to improve the efficiency of ULAR stator blades: The flow phenomena that can be observed are too different to enable exploitation of design principles for high aspect ratio blades directly. Therefore, ULAR stator blades are excellent candidates for numerical optimization. The goal of optimization from the engineering point of view is not only to increase blade efficiency, i.e., ultimately to reduce the engine's fuel consumption, but also to find new design concepts for suppressing the secondary flow loss near the hub-end-wall region and hence to enable control of the three-dimensional nature of the flow. From the optimization point of view 3D aerodynamic design optimization constitutes an interesting problem for several reasons. We have to deal with a high-dimensional search space while evaluation of the objective function is so costly that an appropriate acquisition of data from the search space is hardly feasible. This means that we have to use techniques that reduce the dimensionality of the search space as much as possible and we have to use algorithms that are able to cope with extremely sparse data. Also the formulation of the optimization objective is not as obvious as it may seem. Traditionally, the minimization of the aerodynamic loss, i.e., the average pressure loss, is chosen as optimization target. However, we must not forget that this is an extreme simplification of the problem. In fact, the pressure loss is only one among many quantities that an engineer takes into account when assessing the blade performance. To compound matters, three-dimensional aerodynamic flow is not fully understood yet, so that it is difficult to foresee the effects that may result from the choice of a particular combination of optimization objectives. In this paper, we consider two formulations of the objective function. As a first guess we use the single objective of minimization of the mass-averaged total pressure loss. While this yields satisfactory results, we found that it is desirable to include a second objective, the minimization of the variation of the circumferential static pressure distribution. This renders the problem multi-objective. As a first approach we address the multi-objective optimization problem in the simplest way, namely by linear aggregation of the two objectives. Three-dimensional design optimization is not only an interesting problem from the engineering and optimization point of view but also from a technical point of view the design of a stable and fault tolerant computing environment that includes a whole bunch of computers and a variety of software components is a challenge. In this paper, we will discuss 3D aerodynamic design optimization from all three above mentioned perspectives. In Sec. 2 we present the ultra-low-aspect-ratio transonic stator blades that will be optimized. In Sec. 3, we discuss the components of the optimization problem, i.e., the choice of blade model, the formulation of the fitness function, and the architecture of the simulation environment. The optimization results are presented and discussed in Sec. 4. Finally, our conclusions are given in Sec. 5. In this paper, we applied an evolutionary algorithm, namely CMA-ES, to the solution of a large scale, complex, real world optimization problem. We described the simulation environment that we developed to solve aerodynamic optimization problems and demonstrated the feasibility of our approach. From an aerodynamic point of view one goal of using design optimization instead of resorting to traditional engineering knowledge for aerodynamic blade design is to identify new design concepts from the optimization results. This goal was achieved in this study and we can draw the following conclusions:. (i) The optimization resulted in a blade with a noticeable bent part near the trailing edge. This extremely aftloaded blade is effective for the reduction of secondary losses.. (ii) The flow mechanism for reducing the secondary flow loss seems to be the reduction of the pitch-wise driving force resulting in a reduced migration of low momentum fluid near the tip and/or hub casing around the mid-axial chord position.. (iii) This leads to a considerably delayed development of the boundary layer on the suction surface.. From the optimization point of view the combination of the different criteria and constraints constitute an interesting problem. In particular the relation between the pressure loss and the variation of the static outlet pressure deserves further attention. The trade-off relation between both objectives has been previously pointed out in the literature [13] . In this paper, we employed the simplest way to combine the two objectives, namely linear aggregation. Its advantage is that the problem remains single objective and more efficient algorithms can be used than are available for multi-objective optimization. The drawback is -besides the linearity of the combination -the ad-hoc choice of the relative weights. Indeed as our results show, the static pressure variation has received too much attention during the optimization. In other words, the selection pressure toward smaller pressure loss values was not sufficient. There are two principle ways to proceed. First, we can avoid the combination of both objectives and use multi-objective optimization methods [4, 3] to determine the Pareto front. Second, we can render the second criterion a constraint. Thus, we set the variation of the static outlet pressure of the baseline blade as a soft constraint, so that slight overshooting is penalized only slightly, and solve the remaining single objective optimization problem of minimizing only the pressure loss. We intend to follow both pathways in future optimizations. Another topic for future research is the representation of the blade model. In this study, we used a B-spline surface representation. However, the number of control points necessary to achieve sufficient flexibility with this kind of model may become unfeasibly large since this number directly determines the dimension of the search space and hence the convergence time of the optimization algorithm. This tradeoff between the flexibility of the model and the search space dimension cannot be resolved easily if the representation is static. Instead, a dynamic and adaptive representation is required as proposed in [11] .

O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Low-Complexity Policies for Energy-Performance Tradeoff in Chip-Multi-Processors Abstract-Chip-multi-processor (CMP) utilize multiple energy-efficient processing elements (PEs) to deliver high performance while reducing energy-consumption. Dynamic frequency-Voltage Scaling (DVS) balances performance and energy consumption by varying PEs' frequency-voltage workpoints to save energy while meeting performance requirements. We consider multi-task CMP applications with unknown workloads, and dynamically set workpoints to minimize ET . Heuristic policies for serial/parallel task-graphs are investigated. We compare these policies to a theoretical bound and show that they achieve good results with low complexity. In most cases the simplest policy, which usually assigns constant workpoints, is also the most cost-effective one.Index Terms-Chip-multi-processor (CMP), dynamic voltage scaling, low power, slack utilization. Chip-multi-processor (CMP) architectures integrate multiple relatively small energy-efficient processing elements (PEs), to enable energy-efficient performance scaling [1] - [3] . Dynamic frequency-Voltage Scaling (DVS) is a widely practiced [4] and researched [5] technique for energy-performance tradeoff in which a PE's frequency is altered dynamically to meet performance requirements while consuming limited energy. The supply voltage of each PE is kept at the lowest feasible value for the selected frequency. Scaling the frequency-voltage workpoint (f; V ) can result in near-quadratic energy savings [6] .. In a CMP running multiple dependent tasks, DVS may save energy without degrading performance. At any given time, one or few tasks typically constitute(s) the performance bottleneck while other PEs can be slowed down without affecting total performance. We refer to slowing down non-critical tasks in CMP as slack-utilization [7] , [8] .. When task workloads are known in advance, the DVS policy sets workpoints to utilize precisely all available slack. But when task workloads are unknown in advance, slack-utilization is nontrivial. Assuming worst-case workloads achieves limited energy savings since overly aggressive workpoints are needed. Conversely, overestimating slack can lead to performance degradation. Workload estimation is a primary factor of the efficiency of DVS policies. Measuring DVS policy efficiency depends on the energy/power/performance requirements of target applications. Mobile battery-operated systems strive to extend battery life, while desktop systems and servers typically optimize power rather than energy. While a maximum performance system would always run at the maximum frequency (the f -max policy), a minimal energy system should execute at the minimum frequency (the f -min policy). A system which strives to balance energy and performance could maneuver (f; V ) between justifiable energy consumption at the high end and tolerable performance at the low end. This choice is reflected in the criterion selected to assess alternative DVS policies.. If the required calculations for policy implementation are to be integrated into the system itself and performed in real-time, then it is essential that energy-consumption and delay of the policy calculation itself be minimal. Spending a substantial amount of execution time and energy merely to calculate workpoints may considerably offset the savings aimed at, making it impractical for a performance-and energy-aware system. Thus, low computational complexity is a key concern.. Previous DVS policies [9] - [12] for CMP attempt to formulate optimization problems which have high computational complexity. In contrast, we introduce lightweight heuristic policies, and show that they achieve good results compared to theoretical bounds. We further show that in most cases the simplest policy is the most cost-effective one.. This paper is organized as follows. Section II defines the minimization criterion and formulates the DVS minimization problem. The DVS policies are presented in Section III, and analyzed in Section IV. Conclusions are drawn in Section V.. Embedded semiconductor memories tend to play an increasingly important role in the operation of integrated circuits and systems. Since advances in memory technology tend to make memory devices more and more complicated (due to the appearance of new defect mechanisms), considerable effort has been put to the direction of efficiently testing such modules [1] - [4] , [14] - [21] . RAMs are typically discerned into bit-and word-organized [4] .. For the testing of embedded RAMs, march algorithms outperform competitive schemes, since they result in simple, yet effective, testing scenarios [5] . A march algorithm comprises a series of march elements that perform a predetermined sequence of operations (read and/or write) in every cell (for the case of bit-organized RAMs) or word (for the case of word-organized RAMs).. Testing of RAM modules is performed both right after manufacturing and periodically in the field. During manufacturing testing, various kinds of tests are applied in order to ensure that the RAM operates normally; typical tests applied during manufacturing testing are march tests. Traditional march algorithms, e.g., [5] - [7] , start with an initial write-all-zero phase, where all the RAM cells are set to 0 in order to ensure that the final signature in the output compactor is known [5] .. Periodic testing is discerned into start-up testing and testing during normal operation. Start-up testing is performed during the start-up of the system and resembles manufacturing testing. In testing during normal operation, the RAM normal operation is stalled (i.e., set out of normal operation), tested and then given back to operation. This kind of testing is applied to circuits where it is difficult and/or impractical to shut down the system since the contents of the RAM cannot be lost. In this kind of testing, traditional march tests cannot be applied since (due to the initial write-all zero phase) the contents of the RAM cells before the test are lost.. In order to confront the previously mentioned problems, transparent built-in self test (BIST) was proposed by Nicolaidis [1] ; in a transparent BIST algorithm, the initial write-all-zero phase is skipped; instead, a signature prediction phase is issued that precedes the normal march series. During this signature prediction phase, a signature is captured and stored. In the sequel, a sequence of carefully selected read and write operations are performed, that leave the RAM contents equal to the initial ones with the same fault coverage of the corresponding traditional march algorithm; the final signature is compared to the one captured during the signature prediction phase and a decision is made as to whether a fault has occurred in the RAM or not. The concept of transparent BIST is further analyzed in Section II-B.. Yarmolik et al. [8] , [9] advanced the field proposing the concept of symmetric transparent BIST. In symmetric transparent BIST, the signature prediction phase is skipped and the march series is modified in such a way that the final signature is equal to the all-zero state, irrespectively of the RAM initial contents. For response compaction of bit organized RAM's, in [8] a single-input shift register (SISR) was utilized whose characteristic polynomial toggles between a primitive polynomial and its reciprocal one during the different march elements of the march series. For the case of word-organized RAMs, it was proven in [9] that a multiple-input shift register (MISR) whose characteristic polynomial is altered in a similar fashion could serve as response compactor for symmetric transparent BIST, resulting in a predetermined (all-zero) state. The concept of symmetric transparent BIST is analyzed and exemplified in Section II-C.. The work of Yarmolik et al., although revolutionary, requires modifying existing registers (or SISRs/MISRs) in order to serve as response evaluators and requires complicated control logic in such way to toggle between the two different polynomials during the application of the march series.. It is widely accepted by the test community that the utilization of modules that typically exist in the circuit, e.g., accumulators [10] or arithmetic logic units (ALUs) [11] , for BIST test pattern generation and/or response verification possesses advantages, such as lower hardware overhead and elimination of the need for multiplexers in the circuit path; furthermore, the modules are exercised, therefore, faults existing in them can be discovered [12] .. In this paper, we propose the use of accumulator-based compaction in symmetric transparent RAM BIST (ASTRA). In modules that contain accumulators, the output of the RAM is either directly driven to the accumulator inputs or can be driven using processor instructions. It is shown that the proposed scheme imposes lower hardware overhead In this paper, a new integrated one-cycle controlled switching converter is presented. To allow using standard low-cost CMOS process and to achieve fast transient response, a non-inverting SC integrator is employed. Tight load regulation was achieved with the use of an additional outer loop. Experimental results show very competitive performances in power converter design matrix. Furthermore, the design techniques can be applied to other DC-DC or AC-DC converters. In this paper, we presented several DVS policies for CMPs, and demonstrated that simple policies achieve good results compared to more complex ones, and are within approximately 35% of optimal bounds. We started by formulating an energy-performance optimization problem of an application running on a CMP and noted the complexity of the problem, which makes it impractical for implementation. As an alternative, we described several heuristic DVS policies which utilize available time-slack to save energy in a performanceaware manner: Constant, Interval, and Multi-PACE. The frequencyinvariant criterion was employed for comparing the policies. Except for isolated cases, all policies reach comparable results. Increasing the number of re-estimations (using Interval) bears only a marginal improvement. Multi-PACE produces results that are anywhere between Interval and Constant, depending on the distribution. Since the results are usually quite close for all policies, we conclude that the least complex policy, Constant, is usually preferred. Use of Interval is justified only for certain distributions which highly benefit from re-estimation, and should be weighed against the added complexity. Based on these findings, a scheme could be contemplated whereby the number of intervals is chosen dynamically based on certain characteristics of the distribution or on past results. Multi-PACE generally does not achieve better results than any of the other two, and thus is not preferred due to its high complexity.. Taking workpoint transitions into account may degrade the results since each transition incurs performance and energy penalties [9] . When transition costs are considered, simple policies such as Constant become even more attractive because they employ fewer transitions.. Several topics are proposed for future research. More complex task graphs may be considered. Discrete (f; V ) workpoints could be studied. The Interval policy may be enhanced to consider re-estimation at flexible times. Test cases based on real application traces can be employed. Applications may be modified to estimate their own remaining work.

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