wanyu/IteraTeR_full_sent huggingface dataset:
Original:  This paper proposes new learning algorithms in two-player zero-sum  games where the number of pure strategies is huge or even infinite . Specifically, we combine no-regret analysis from online learning with double oracle methods from game theory.
Revised:  This paper proposes new learning algorithms in two-player zero-sum games where the number of pure strategies is prohibitively large . Specifically, we combine no-regret analysis from online learning with double oracle methods from game theory.
Edit intent: clarity
Original:  This paper proposes new learning algorithms in two-player zero-sum  games where the number of pure strategies is huge or even infinite . Specifically, we combine no-regret analysis from online learning with double oracle methods from game theory.
Revised:  This paper proposes new learning algorithms in two-player zero-sum games where the number of pure strategies is huge or even infinite . Specifically, we combine no-regret analysis from online learning with Double Oracle (DO) methods from game theory.
Edit intent: clarity
Original:  Our method -- Online Double Oracle (ODO) -- achieves the  regret bound of \mathcal{O}(\sqrt{T k \log(k)}) in self-play setting where k is NOT the size of the game , but rather the size of \emph{effective strategy set} that is linearly dependent on the support size of the Nash equilibrium .
Revised:  Our method -- Online Double Oracle (ODO) -- is provably convergent to a Nash equilibrium (NE). Most importantly, unlike normal DO methods, ODO is regret bound of \mathcal{O}(\sqrt{T k \log(k)}) in self-play setting where k is NOT the size of the game , but rather the size of \emph{effective strategy set} that is linearly dependent on the support size of the Nash equilibrium .
Edit intent: meaning-changed
Original:  Our method -- Online Double Oracle (ODO) -- achieves the  regret bound of \mathcal{O}(\sqrt{T k \log(k)}) in self-play setting where k is NOT the size of the game , but rather the size of \emph{effective strategy set} that is linearly dependent on the support size of the Nash equilibrium .
Revised:  Our method -- Online Double Oracle (ODO) -- achieves therationale regret bound of \mathcal{O}(\sqrt{T k \log(k)}) in self-play setting where k is NOT the size of the game , but rather the size of \emph{effective strategy set} that is linearly dependent on the support size of the Nash equilibrium .
Edit intent: meaning-changed
Original:  Our method -- Online Double Oracle (ODO) -- achieves the  regret bound of \mathcal{O}(\sqrt{T k \log(k)}) in self-play setting where k is NOT the size of the game , but rather the size of \emph{effective strategy set} that is linearly dependent on the support size of the Nash equilibrium .
Revised:  Our method -- Online Double Oracle (ODO) -- achieves the in the sense that each agent in ODO can exploit strategic adversary with a regret bound of \mathcal{O}(\sqrt{T k \log(k)}) in self-play setting where k is NOT the size of the game , but rather the size of \emph{effective strategy set} that is linearly dependent on the support size of the Nash equilibrium .
Edit intent: meaning-changed
Original:  Our method -- Online Double Oracle (ODO) -- achieves the  regret bound of \mathcal{O}(\sqrt{T k \log(k)}) in self-play setting where k is NOT the size of the game , but rather the size of \emph{effective strategy set} that is linearly dependent on the support size of the Nash equilibrium .
Revised:  Our method -- Online Double Oracle (ODO) -- achieves the regret bound of \mathcal{O}(\sqrt{T k \log(k)}) where k is NOT the size of the game , but rather the size of \emph{effective strategy set} that is linearly dependent on the support size of the Nash equilibrium .
Edit intent: clarity
Original:  Our method -- Online Double Oracle (ODO) -- achieves the  regret bound of \mathcal{O}(\sqrt{T k \log(k)}) in self-play setting where k is NOT the size of the game , but rather the size of \emph{effective strategy set} that is linearly dependent on the support size of the Nash equilibrium .
Revised:  Our method -- Online Double Oracle (ODO) -- achieves the regret bound of \mathcal{O}(\sqrt{T k \log(k)}) in self-play setting where k is not the total number of pure strategies , but rather the size of \emph{effective strategy set} that is linearly dependent on the support size of the Nash equilibrium .
Edit intent: meaning-changed
Original:  Our method -- Online Double Oracle (ODO) -- achieves the  regret bound of \mathcal{O}(\sqrt{T k \log(k)}) in self-play setting where k is NOT the size of the game , but rather the size of \emph{effective strategy set} that is linearly dependent on the support size of the Nash equilibrium .
Revised:  Our method -- Online Double Oracle (ODO) -- achieves the regret bound of \mathcal{O}(\sqrt{T k \log(k)}) in self-play setting where k is NOT the size of the game , but rather the size of \emph{effective strategy set} that is linearly dependent on the support size of the NE .
Edit intent: clarity
Original:  On tens of different real-world games, including Leduc Poker that contains 3^{936 no-regret algorithms and double oracle methods by a large margin, both in  convergence rate to Nash equilibrium and average payoff against strategic adversary .
Revised:  On tens of different real-world games, ODO outperforms DO, PSRO methods, and no-regret algorithms and double oracle methods by a large margin, both in convergence rate to Nash equilibrium and average payoff against strategic adversary .
Edit intent: meaning-changed
Original:  On tens of different real-world games, including Leduc Poker that contains 3^{936 no-regret algorithms and double oracle methods by a large margin, both in  convergence rate to Nash equilibrium and average payoff against strategic adversary .
Revised:  On tens of different real-world games, including Leduc Poker that contains 3^{936 no-regret algorithms such as Multiplicative Weight Update by a significant margin, both in convergence rate to Nash equilibrium and average payoff against strategic adversary .
Edit intent: meaning-changed
Original:  On tens of different real-world games, including Leduc Poker that contains 3^{936 no-regret algorithms and double oracle methods by a large margin, both in  convergence rate to Nash equilibrium and average payoff against strategic adversary .
Revised:  On tens of different real-world games, including Leduc Poker that contains 3^{936 no-regret algorithms and double oracle methods by a large margin, both in terms of convergence rate to Nash equilibrium and average payoff against strategic adversary .
Edit intent: clarity
Original:  On tens of different real-world games, including Leduc Poker that contains 3^{936 no-regret algorithms and double oracle methods by a large margin, both in  convergence rate to Nash equilibrium and average payoff against strategic adversary .
Revised:  On tens of different real-world games, including Leduc Poker that contains 3^{936 no-regret algorithms and double oracle methods by a large margin, both in convergence rate to a NE and average payoff against strategic adversary .
Edit intent: clarity
Original:  On tens of different real-world games, including Leduc Poker that contains 3^{936 no-regret algorithms and double oracle methods by a large margin, both in  convergence rate to Nash equilibrium and average payoff against strategic adversary .
Revised:  On tens of different real-world games, including Leduc Poker that contains 3^{936 no-regret algorithms and double oracle methods by a large margin, both in convergence rate to Nash equilibrium and average payoff against strategic adversaries .
Edit intent: fluency
Original:  Motivated by the problem of computing the homology of this bifiltration, we introduce two closely related combinatorial bifiltrations, one simplicial and the other polyhedral , which are both topologically equivalent to the multicover bifiltration and far smaller than a \v{C model considered in prior work of Sheehy.
Revised:  Motivated by the problem of computing the homology of this bifiltration, we introduce two closely related combinatorial bifiltrations, one polyhedral and the other polyhedral , which are both topologically equivalent to the multicover bifiltration and far smaller than a \v{C model considered in prior work of Sheehy.
Edit intent: fluency
Original:  Motivated by the problem of computing the homology of this bifiltration, we introduce two closely related combinatorial bifiltrations, one simplicial and the other polyhedral , which are both topologically equivalent to the multicover bifiltration and far smaller than a \v{C model considered in prior work of Sheehy.
Revised:  Motivated by the problem of computing the homology of this bifiltration, we introduce two closely related combinatorial bifiltrations, one simplicial and the other simplicial , which are both topologically equivalent to the multicover bifiltration and far smaller than a \v{C model considered in prior work of Sheehy.
Edit intent: clarity
Original:  Motivated by the problem of computing the homology of this bifiltration, we introduce two closely related combinatorial bifiltrations, one simplicial and the other polyhedral , which are both topologically equivalent to the multicover bifiltration and far smaller than a \v{C model considered in prior work of Sheehy.
Revised:  Motivated by the problem of computing the homology of this bifiltration, we introduce two closely related combinatorial bifiltrations, one simplicial and the other polyhedral , which are both topologically equivalent to the multicover bifiltration and far smaller than a \v Cech-based model considered in prior work of Sheehy.
Edit intent: meaning-changed
Original:  Our polyhedral construction is a variant of the rhomboid tiling of Edelsbrunner and Osang, and can be efficiently computed using a variant of an algorithm given by these authors.
Revised:  Our polyhedral construction is a bifiltration of the rhomboid tiling of Edelsbrunner and Osang, and can be efficiently computed using a variant of an algorithm given by these authors.
Edit intent: meaning-changed
Original:  The proposed system combines merits from VIO and GNSS system, thus is able to achieve both local smoothness and global consistency. To associate global measurements with local states, a coarse-to-fine initialization procedure is proposed to efficiently online calibrate the transformation and initialize GNSS states from only a short window of measurements.
Revised:  Our system is aiming to provide accurate global 6-DoF estimation under complex indoor-outdoor environment where GNSS signals may be largely intercepted or even totally unavailable. To connect global measurements with local states, a coarse-to-fine initialization procedure is proposed to efficiently online calibrate the transformation and initialize GNSS states from only a short window of measurements.
Edit intent: meaning-changed
Original:  Thanks to the tightly-coupled multi-sensor approach and system design, our estimator is able to recover the position and orientation in the global Earth frame, even with less than 4 satellites being tracked .
Revised:  Thanks to the tightly-coupled multi-sensor approach and system design, our system fully exploits the merits of three types of sensors and is capable to seamlessly cope with the transition between indoor and outdoor environments, where satellites are lost and recaptured again .
Edit intent: meaning-changed
Original:  We extensively evaluate the proposed system on simulation and real-world experiments, and the result demonstrates that our system substantially eliminates the drift of VIO and preserves the  accuracy in spite of noisy GNSS measurements  .
Revised:  We extensively evaluate the proposed system by both simulation and real-world experiments, and the result demonstrates that our system substantially eliminates the drift of VIO and preserves the accuracy in spite of noisy GNSS measurements .
Edit intent: clarity
Original:  We extensively evaluate the proposed system on simulation and real-world experiments, and the result demonstrates that our system substantially eliminates the drift of VIO and preserves the  accuracy in spite of noisy GNSS measurements  .
Revised:  We extensively evaluate the proposed system on simulation and real-world experiments, and the result demonstrates that our system substantially eliminates the drift of VIO and preserves the local accuracy in spite of noisy GNSS measurements .
Edit intent: meaning-changed
Original:  We extensively evaluate the proposed system on simulation and real-world experiments, and the result demonstrates that our system substantially eliminates the drift of VIO and preserves the  accuracy in spite of noisy GNSS measurements  .
Revised:  We extensively evaluate the proposed system on simulation and real-world experiments, and the result demonstrates that our system substantially eliminates the drift of VIO and preserves the accuracy in spite of noisy GNSS measurements . In addition, experiments also show that our system can gain from even a single satellite while conventional GNSS algorithms need four at lease .
Edit intent: meaning-changed
Original:  Among three newly identified fast-growing RBD mutations, L452R  and N501T are able to effectively weaken the binding of many known antibodies with the RBD.
Revised:  Among three newly identified fast-growing RBD mutations, L452R , which is now known as part of the California variant B.1.427, and N501T are able to effectively weaken the binding of many known antibodies with the RBD.
Edit intent: meaning-changed
Original:  Our comprehensive genetic analysis and protein-protein binding study show that the genetic evolution of SARS-CoV-2 on the RBD, which may be regulated by host gene editing, viral proofreading, random genetic drift, and natural selection, gives rise to more infectious variants that will potentially compromise existing vaccines and antibody therapies .
Revised:  Finally, we hypothesize that RBD mutations that can simultaneously make SARS-CoV-2 on the RBD, which may be regulated by host gene editing, viral proofreading, random genetic drift, and natural selection, gives rise to more infectious variants that will potentially compromise existing vaccines and antibody therapies .
Edit intent: meaning-changed
Original:  Our comprehensive genetic analysis and protein-protein binding study show that the genetic evolution of SARS-CoV-2 on the RBD, which may be regulated by host gene editing, viral proofreading, random genetic drift, and natural selection, gives rise to more infectious variants that will potentially compromise existing vaccines and antibody therapies .
Revised:  Our comprehensive genetic analysis and protein-protein binding study show that the genetic evolution of SARS-CoV-2 more infectious and disrupt the existing antibodies, called vaccine escape mutations, will pose an imminent threat to the current crop of vaccines. A list of most likely vaccine escape mutations is given, including N501Y, L452R, E484K, N501T, S494P, and K417N .
Edit intent: meaning-changed
Original:  Such processing is often associated with Bayesian inference. Yet most common models of neural cells , including biologically plausible, such as Hodgkin-Huxley or Izhikevich  do not possess predictive dynamics on the level of a single cell.
Revised:  However, most common neural cell models , including biologically plausible, such as Hodgkin-Huxley or Izhikevich do not possess predictive dynamics on the level of a single cell.
Edit intent: coherence
Original:  Yet most common models of neural cells , including biologically plausible, such as Hodgkin-Huxley or Izhikevich  do not possess predictive dynamics on the level of a single cell.
Revised:  Yet most common models of neural cells , including biologically plausible, such as Hodgkin-Huxley or Izhikevich , do not possess predictive dynamics on the level of a single cell.
Edit intent: fluency
Original:  Yet most common models of neural cells , including biologically plausible, such as Hodgkin-Huxley or Izhikevich  do not possess predictive dynamics on the level of a single cell. The modern rules of synaptic plasticity or interconnections weights adaptation also do not provide grounding for the ability of neurons to adapt to the ever-changing input signal intensity.
Revised:  Yet most common models of neural cells , including biologically plausible, such as Hodgkin-Huxley or Izhikevich do not possess predictive dynamics on a single-cell level. Moreover, the modern rules of synaptic plasticity or interconnections weights adaptation also do not provide grounding for the ability of neurons to adapt to the ever-changing input signal intensity.
Edit intent: coherence
Original:  In the present article , we will introduce new mechanics of interconnection between neuron firing rate homeostasis and weight change by means of STDP growth bounded by abstract protein reserve, controlled by the intracellular optimization algorithm.
Revised:  The present article introduces new mechanics of interconnection between neuron firing rate homeostasis and weight change by means of STDP growth bounded by abstract protein reserve, controlled by the intracellular optimization algorithm.
Edit intent: coherence
Original:  In the present article , we will introduce new mechanics of interconnection between neuron firing rate homeostasis and weight change by means of STDP growth bounded by abstract protein reserve, controlled by the intracellular optimization algorithm.
Revised:  In the present article , we will introduce new mechanics of interconnection between neuron firing rate homeostasis and weight change through STDP growth bounded by abstract protein reserve, controlled by the intracellular optimization algorithm.
Edit intent: clarity
Original: We provide a theory of strategic interactions in static games in the presence of ignorance, i.e., when players cannot produce beliefs as probability measures (or similia) concerning the uncertain elements present in the interaction they are involved in.
Revised: Assuming only ordinal preferences as transparent, we study players interacting under the veil of ignorance, i.e., when players cannot produce beliefs as probability measures (or similia) concerning the uncertain elements present in the interaction they are involved in.
Edit intent: meaning-changed
Original: We provide a theory of strategic interactions in static games in the presence of ignorance, i.e., when players cannot produce beliefs as probability measures (or similia) concerning the uncertain elements present in the interaction they are involved in. Assuming only players ' ordinal preferences as transparent, we investigate players that are either optimistic or pessimistic, that we deem tropicalplayers. To explicitly formalize these attitudes , we employ tools from interactive epistemology, by defining the corresponding epistemic events in epistemic possibility structures, which are the counterpart of epistemic type structures suited for our analysis in the presence of ignorance, We show that the behavioral implications related to common belief in these events have algorithmic counterparts in terms of iterative deletion procedures.
Revised: We provide a theory of strategic interactions in static games in the presence of ignorance, i.e., when players cannot produce beliefs as probability measures but rather have coarse beliefs represented as subsets of opponents' actions. These players follow either \max \max or \max \min decision criteria. The criteria can be identified as optimistic and pessimistic attitudes, respectively, which we refer to as ``tropical''. Explicitly formalizing these attitudes and how players reason under ignorance, we characterize the behavioral implications related to common belief in these events have algorithmic counterparts in terms of iterative deletion procedures.
Edit intent: clarity
Original:  To explicitly formalize these attitudes , we employ tools from interactive epistemology, by defining the corresponding epistemic events in epistemic possibility structures, which are the counterpart of epistemic type structures suited for our analysis in the presence of ignorance, We show that the behavioral implications related to common belief in these events have algorithmic counterparts in terms of iterative deletion procedures. While optimism is related to Point Rationalizability, to capture pessimism we introduce a new algorithm , deemed Wald Rationalizability .
Revised:  To explicitly formalize these attitudes , we employ tools from interactive epistemology, by defining the corresponding epistemic events in epistemic possibility structures, which are the counterpart of epistemic type structures suited for our analysis in the presence of ignorance, We show that the behavioral implications related to common belief in these events : while optimism is related to Point Rationalizability, to capture pessimism we introduce a new algorithm , deemed Wald Rationalizability .
Edit intent: clarity
Original:  While optimism is related to Point Rationalizability, to capture pessimism we introduce a new algorithm , deemed Wald Rationalizability . We show that the algorithmic procedure capturing optimism selects a subset of the strategies selected by the algorithmic procedure capturing pessimism. Additionally, we compare both algorithmic procedures to an analogous algorithm based on URLers dominance, deemed URLers Rationalizability, and we show that in generic static games both Point Rationalizability and Wald Rationalizability select a subset of the actions selected by URLers Rationalizability. More generally, while we prove that dropping the genericity assumption does not change the relation between Point Rationalizability and URLers Rationalizability, we show that Wald and URLers Rationalizability are not comparable in their behavioral implications, and we shed light on why this difference emerges.
Revised:  While optimism is related to Point Rationalizability, to capture pessimism we introduce a new algorithm -- Wald Rationalizability -- captures pessimism. Our characterizations allow us to uncover novel connections and results: (i) regarding optimism, we prove that dropping the genericity assumption does not change the relation between Point Rationalizability and URLers Rationalizability, we show that Wald and URLers Rationalizability are not comparable in their behavioral implications, and we shed light on why this difference emerges.
Edit intent: coherence
Original:  More generally, while we prove that dropping the genericity assumption does not change the relation between Point Rationalizability and URLers Rationalizability, we show that Wald and URLers Rationalizability are not comparable in their behavioral implications, and we shed light on why this difference emerges.
Revised:  More generally, while we prove that dropping the (implicit) assumption that whatever a player believes is also true allows to capture wishful thinking \`a la Yildiz (2007), thus reversing an existence failure described therein; (ii) by studying how pessimism and optimism relate to URLers dominance, we shed light on why this difference emerges.
Edit intent: meaning-changed
Original:  More generally, while we prove that dropping the genericity assumption does not change the relation between Point Rationalizability and URLers Rationalizability, we show that Wald and URLers Rationalizability are not comparable in their behavioral implications, and we shed light on why this difference emerges. Finally, we explore connections to strategic wishful thinking .
Revised:  More generally, while we prove that dropping the genericity assumption does not change the relation between Point Rationalizability and URLers Rationalizability, we show that Wald and URLers Rationalizability are not comparable in their behavioral implications, and we shed light on the appropriate notion of rationality in ordinal games; (iii) finally, with respect to pessimism, our analysis identifies Wald Rationalizability as the limit point of players becoming infinitely risk averse, hence, clarifying the conceptual underpinnings behind a discontinuity in the analysis of Rationalizability in presence of varying risk attitudes hinted in Weinstein (2016) .
Edit intent: meaning-changed